{"id":26803,"date":"2021-06-13T13:00:22","date_gmt":"2021-06-13T13:00:22","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26803"},"modified":"2024-05-22T04:00:55","modified_gmt":"2024-05-22T04:00:55","slug":"%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%9a%e0%a4%b0-%e0%a4%94%e0%a4%b0-%e0%a4%b8%e0%a4%82%e0%a4%ad%e0%a4%be%e0%a4%b5%e0%a5%8d%e0%a4%af%e0%a4%a4%e0%a4%be-%e0%a4%b5%e0%a4%bf%e0%a4%a4","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%9a%e0%a4%b0-%e0%a4%94%e0%a4%b0-%e0%a4%b8%e0%a4%82%e0%a4%ad%e0%a4%be%e0%a4%b5%e0%a5%8d%e0%a4%af%e0%a4%a4%e0%a4%be-%e0%a4%b5%e0%a4%bf%e0%a4%a4\/","title":{"rendered":"\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 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\u0907\u0938\u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u094b\u0964 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0926\u094b \u091a\u0930 \u090f\u0915 \u0939\u0940 \u0935\u093f\u0924\u0930\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u090f\u0915 \u0939\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0928\u0939\u0940\u0902\u0964<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:\n<\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e: \u091b\u093e\u0924\u094d\u0930 \u092f\u0939 \u0935\u0930\u094d\u0923\u0928 \u0914\u0930 \u0938\u092e\u091d\u093e \u0938\u0915\u0947\u0902\u0917\u0947 \u0915\u093f \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094d\u092f\u093e \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0915\u0948\u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e: \u091b\u093e\u0924\u094d\u0930 \u092f\u0939 \u0938\u092e\u091d\u093e \u0938\u0915\u0947\u0902\u0917\u0947 \u0915\u093f \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u094d\u092f\u093e \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0947\u0902<\/strong> \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e: \u091b\u093e\u0924\u094d\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092e\u0941\u0916\u094d\u092f \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u094b \u092a\u0939\u091a\u093e\u0928 \u0914\u0930 \u0935\u0930\u094d\u0923\u0928 \u0915\u0930 \u0938\u0915\u0947\u0902\u0917\u0947\u0964<\/li>\n<li><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902<\/strong> \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927: \u091b\u093e\u0924\u094d\u0930 \u092f\u0939 \u0938\u092e\u091d \u0938\u0915\u0947\u0902\u0917\u0947 \u0915\u093f \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0948\u0938\u0947 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902, \u0914\u0930 \u0915\u0948\u0938\u0947 \u0926\u094b \u091a\u0930 \u090f\u0915 \u0939\u0940 \u0935\u093f\u0924\u0930\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u090f\u0915 \u0939\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0928\u0939\u0940\u0902\u0964<\/li>\n<li><strong>\u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0947\u0902<\/strong> \u0914\u0930 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902: \u091b\u093e\u0924\u094d\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930 \u0938\u0915\u0947\u0902\u0917\u0947 \u0914\u0930 \u0907\u0928 \u0917\u0941\u0923\u0927\u0930\u094d\u092e\u094b\u0902 \u0915\u094b \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0932\u093e\u0917\u0942 \u0915\u0930 \u0938\u0915\u0947\u0902\u0917\u0947\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e: \u091b\u093e\u0924\u094d\u0930 \u092f\u0939 \u0935\u0930\u094d\u0923\u0928 \u0915\u0930 \u0938\u0915\u0947\u0902\u0917\u0947 \u0915\u093f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f \u0915\u094d\u092f\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u0935\u093f\u0937\u092f-\u0938\u0942\u091a\u0940<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/strong><\/a><br \/>\n<a href=\"#3\">\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e<\/a><br \/>\n<a href=\"#4\">\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927<\/a><br \/>\n<\/center><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/gIKn9t1hnrw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0914\u0930 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0947 \u092e\u0941\u0916\u094d\u092f \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u091c\u094b \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u092e\u0928\u0947 \u0905\u092c \u0924\u0915 \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u093f\u092f\u093e \u0939\u0948, \u0935\u0939 \u090f\u0915 \u0905\u0930\u094d\u0925 \u092e\u0947\u0902 \u00ab\u092a\u0942\u0930\u094d\u0923\u00bb \u0939\u0948, \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915\u0924\u093e \u092f\u0939 \u0939\u0948 \u0915\u093f \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u092f\u0939 \u0915\u093e\u092b\u0940 \u0906\u0926\u093f\u092e \u0939\u0948; \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923, \u0910\u0938\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0902 \u0939\u0948\u0902 \u091c\u094b \u0939\u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0914\u0930 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0915\u094d\u0937\u092e\u0924\u093e \u0915\u094b \u00ab\u0924\u0947\u0932\u00bb \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><strong><span style=\"color: #ff0000;\">\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f<\/span><\/strong>, \u092f\u0939 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u0939\u092e \u090f\u0915 \u0938\u0939\u091c \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902: \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u00ab\u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u091c\u094b \u090f\u0915 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0940 \u0939\u0948\u00bb \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u090f\u0915 \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u0938\u092e\u091d \u0915\u0947 \u0932\u093f\u090f, \u0907\u0938\u0915\u093e \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u092d\u0940 \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0906\u0907\u090f \u0907\u0938 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u094b \u0926\u0947\u0916\u0947\u0902:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><\/span> \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{X}<\/span><\/span> \u092a\u0930 \u090f\u0915 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:\\Omega \\longmapsto \\mathcal{X}<\/span><\/span> \u0939\u0948<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0938\u092c\u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u092e\u0932\u093e \u0924\u092c \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{X}= \\mathbb{R},<\/span><\/span> \u0914\u0930 \u091c\u092c \u0924\u0915 \u0905\u0928\u094d\u092f\u0925\u093e \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e, \u0939\u092e \u0907\u0938\u0947 \u092e\u093e\u0928 \u0932\u0947\u0902\u0917\u0947; \u092f\u093e\u0928\u0940, \u0939\u092e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u092e\u093e\u0928 \u0935\u093e\u0932\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930, \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u092c\u0921\u093c\u0947 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0938\u0947 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X,Y,Z, \\cdots,<\/span><\/span>, \u091c\u092c\u0915\u093f \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u094b \u091b\u094b\u091f\u0947 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0938\u0947 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u0930\u0932\u0924\u093e \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u0915\u0947\u0935\u0932 \u00ab\u091a\u0930\u00bb \u0915\u0939\u0947\u0902\u0917\u0947\u0964<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000000;\"><strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/span> \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f 6 \u092a\u0915\u094d\u0937\u094b\u0902 \u0935\u093e\u0932\u093e \u090f\u0915 \u092a\u093e\u0938\u093e \u0926\u094b \u092c\u093e\u0930 \u092b\u0947\u0902\u0915\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0924\u092c \u0939\u092e\u0947\u0902 \u092f\u0939 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{2d6} = \\{(\\omega_1, \\omega_2)\\;|\\; \\omega_1,\\omega_2 \\in \\{1,2,3,4,5,6\\}\\}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0938\u0947, \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=<\/span><\/span> \u00ab\u090f\u0915 \u0915\u093e \u0906\u0928\u0947 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u00bb<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y=<\/span><\/span> \u00ab\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u00bb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=\\omega_1 + \\omega_2<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Z=<\/span><\/span> \u00ab\u0926\u0942\u0938\u0930\u0947 \u092b\u0947\u0902\u0915\u0928\u0947 \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u00bb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">= \\omega_2<\/span><\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e: <\/strong><\/span><strong><span style=\"color: #ff0000;\">\u090f\u0915 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f (\u092f\u093e \u00abFD\u00bb)<\/span><\/strong> \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0915\u093e \u090f\u0915 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X: \\mathbb{R} \\longmapsto \\mathbb{R}<\/span><\/span> \u0939\u0948, \u091c\u094b \u0938\u0902\u092c\u0902\u0927 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x) = P(\\{\\omega \\;|\\; X(\\omega)\\leq x\\}),<\/span><\/span> \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948, \u092f\u093e \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X\\leq x).<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0906\u092e \u0924\u094c\u0930 \u092a\u0930, \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0909\u0938\u0915\u0940 \u0938\u094d\u092a\u0937\u094d\u091f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u090f\u0915 \u0928\u092e\u0942\u0928\u093e \u0938\u094d\u0925\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span><\/span> \u092e\u0947\u0902 \u0909\u0924\u0928\u0940 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940 \u091c\u093f\u0924\u0928\u0940 \u0915\u093f \u0909\u0938\u0915\u0940 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X<\/span><\/span> \u092e\u0947\u0902 X \u0938\u092c\u0938\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u091f \u0915\u094b \u091b\u094b\u0921\u093c\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u092f\u0926\u093f \u0938\u0902\u0926\u0930\u094d\u092d \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0914\u0930 \u0915\u094b\u0908 \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u092f\u0939 \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0915\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u0939\u0948, \u0905\u0915\u094d\u0938\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim F<\/span><\/span> \u0928\u094b\u091f\u0947\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=gIKn9t1hnrw&amp;t=806s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u090f\u0915 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u0948<\/span><\/strong><\/a> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b<\/span><\/span> \u0915\u094b\u0908 \u092d\u0940 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u092e\u093e\u0928\u094d\u092f \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p style=\"text-align: justify; color: #000000;\">(a) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b \\longrightarrow [P(a\\lt X \\leq b) = F(b) - F(a)]<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(b) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b \\longrightarrow F(a) \\leq F(b),<\/span><\/span> \u092f\u093e\u0928\u0940 \u00abF \u092c\u0922\u093c \u0930\u0939\u093e \u0939\u0948\u00bb\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">(c) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to +\\infty} F(x) = 1<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to -\\infty} F(x) = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(d) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)=\\lim_{t\\to x^+}F(t) - \\lim_{t\\to x^-}F(t)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(e) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F(x)=\\lim_{t\\to x^+}F(t)<\/span><\/span><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\"><span class=\"collapseomatic \" id=\"id69e42d4bd33f8\"  tabindex=\"0\" title=\"\u092a\u094d\u0930\u092e\u093e\u0923\"    >\u092a\u094d\u0930\u092e\u093e\u0923<\/span><div id=\"target-id69e42d4bd33f8\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify; color: #000000;\"><strong>(a)<\/strong> \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u0918\u091f\u0928\u093e\u090f\u0902 \u0939\u0948\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{X\\leq a\\}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{X\\leq b\\}<\/span><\/span> \u0915\u094d\u0930\u092e\u0936\u0903, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925\u0964 \u092f\u0926\u093f \u092f\u0939 \u0938\u092c \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span><\/span> \u0914\u0930 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{P(a\\lt X\\leq b)} = P(B\\setminus A) = P(B) - P(B\\cap A) = P(B)-P(A) =\\color{blue}{F(b) - F(a)}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(b)<\/strong> \u092d\u093e\u0917 (a) \u0938\u0947 \u092f\u0939 \u0928\u093f\u0915\u093e\u0932\u093e \u0917\u092f\u093e \u0939\u0948: \u091a\u0942\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A)\\geq 0,<\/span><\/span> \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(b) - F(a) \\geq 0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u091c\u094b \u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a) \\leq F(b)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(c)<\/strong> \u092f\u0939\u093e\u0901 \u0939\u092e \u0907\u0938 \u0924\u0925\u094d\u092f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u092c\u0922\u093c\u0924\u093e \u0939\u0948 (\u092d\u093e\u0917 (b) \u092e\u0947\u0902 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0917\u092f\u093e) \u0914\u0930 \u00ab1\u00bb \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0940\u092e\u093f\u0924 \u0939\u0948 (\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u093f\u0924\u0930\u0923 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948)\u0964 \u0915\u0947\u0935\u0932 \u0907\u0938\u0938\u0947 \u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty} F(x) = 1<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0915\u093e \u092a\u0942\u0930\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0939\u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0947 \u0938\u093e\u0925 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u0928\u093e\u090f\u0902 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_n=\\{\\omega\\;|\\;X(\\omega)\\leq n\\}.<\/span><\/span> \u0907\u0938\u0938\u0947 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u0948 \u0915\u093f, \u0939\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u0939\u094b\u0917\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_{n}\\subseteq A_{n+1},<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\bigcup_{n\\lt +\\infty} A_n = \\Omega<\/span><\/span> \u0914\u0930 \u0907\u0938\u0932\u093f\u090f, <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%86%d8%b8%d8%b1%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%81%d9%8a%d8%af%d8%a9-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d8%a7%d8%aa\/\" rel=\"noopener\" target=\"_blank\">\u0938\u0924\u0924\u0924\u093e \u0938\u0902\u092a\u0924\u094d\u0924\u093f<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1=P(\\Omega) = P\\left( \\bigcup_{n\\lt +\\infty} A_n \\right) = \\lim_{n\\to +\\infty} P(A_n) = \\lim_{n\\to +\\infty} P(\\{\\omega\\;|\\;X(\\omega)\\leq n\\}) = \\lim_{n\\to +\\infty} P(X\\leq n)=\\lim_{n\\to +\\infty}F(n)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0905\u0930\u094d\u0925\u093e\u0924:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\lim_{x\\to +\\infty} F(x) = 1}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924, \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to -\\infty<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092a\u0939\u0932\u0947 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B_n=\\{\\omega\\;|\\;-n\\lt X(\\omega)\\}.<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u0938\u0947 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{n \\to -\\infty}F(n) = \\lim_{n\\to -\\infty} P(X\\leq n) = \\lim_{n\\to \\infty} P(X\\leq -n)= 1 - \\lim_{n\\to \\infty} P(-n \\lt X) = 1 - \\lim_{n\\to \\infty}P(B_n)) = 1 - P(\\Omega) = 1-1=0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(d)<\/strong> \u0907\u0938\u0947 \u092d\u093e\u0917 (c) \u0915\u0940 \u0924\u0930\u0939 \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle C_n = \\left\\{x - \\frac{1}{n} \\leq X \\leq x + \\frac{1}{n}\\right\\}<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0915\u0947 \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> C_{n+1}\\subseteq C_n<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcap_{n\\gt 0} C_n = \\{X=x\\}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0932\u093f\u090f, <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%86%d8%b8%d8%b1%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%81%d9%8a%d8%af%d8%a9-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d8%a7%d8%aa\/\" rel=\"noopener\" target=\"_blank\">\u0938\u0924\u0924\u0924\u093e \u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u093e \u090f\u0915 \u092a\u0930\u093f\u0923\u093e\u092e<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)=P\\left(\\bigcap_{n\\gt 0} C_n \\right) = \\lim_{n\\to \\infty} P(C_n) = \\lim_{x+1\/n \\to x^+}F\\left(x+1\/n\\right) - \\lim_{x-1\/n \\to x^-}F\\left(x-1\/n\\right)= \\lim_{t \\to x^+}F\\left(t\\right) - \\lim_{t \\to x^-}F\\left(t\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(e)<\/strong> \u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u092e\u093e\u092e\u0932\u093e \u092a\u093f\u091b\u0932\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u091a\u0942\u0902\u0915\u093f \u0939\u092e\u0928\u0947 \u092a\u0939\u0932\u0947 \u0939\u0940 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930 \u0926\u093f\u092f\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)= \\lim_{t \\to x^+}F\\left(t\\right) - \\lim_{t \\to x^-}F\\left(t\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0939\u092e \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{t \\to x^+}F\\left(t\\right) = P(X=x) + \\lim_{t \\to x^-}F\\left(t\\right) = P(X=x) + \\lim_{t\\to x^-}P(X\\leq t)= P(X\\leq x) = F(x)<\/span><\/span><\/p>\n<\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u0910\u0938\u093e \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0926\u094b \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y<\/span><\/span> \u0915\u093e \u0938\u092e\u093e\u0928 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u094b\u0924\u093e \u0939\u0948 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall A\\subseteq \\mathbb{R})(P(X\\in A) = P(Y\\in A)).<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u090f\u0915 \u0939\u0940 \u0928\u092e\u0942\u0928\u093e \u0938\u094d\u0925\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span><\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0926\u094b \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y<\/span><\/span> \u0938\u092e\u093e\u0928 \u0935\u093f\u0924\u0930\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u0932\u093f\u090f \u0935\u0947 \u091c\u0930\u0942\u0930\u0940 \u0928\u0939\u0940\u0902 \u0915\u093f \u090f\u0915 \u0939\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0939\u094b\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0939\u092e \u090f\u0915 \u0938\u0902\u0924\u0941\u0932\u093f\u0924 \u0938\u093f\u0915\u094d\u0915\u0947 \u0915\u0947 \u092b\u0947\u0902\u0915\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u092e\u093e\u0928\u0947\u0902 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=1<\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u094b \u0939\u0947\u0921\u094d\u0938 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=0<\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u094b \u091f\u0947\u0932\u094d\u0938, \u0939\u092e \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y=1-X<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X=1) = P(Y=1)=0.5,<\/span><\/span> \u0914\u0930 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u0928 \u0935\u093f\u0924\u0930\u0923 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092f\u0926\u093f \u0939\u092e \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u0928 \u092e\u093e\u0928 \u0939\u094b\u0928\u0947 \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e \u0915\u094d\u092f\u093e \u0939\u0948, \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X=Y)=0<\/span><\/span><\/p>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0915\u093f \u0939\u092e \u0938\u092e\u091d\u0947\u0902 \u0915\u093f \u0915\u0948\u0938\u0947 \u092f\u0947 \u0926\u094b \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0902 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902\u0964 \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u092f\u0939 \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u0926\u094b \u091a\u0930 \u090f\u0915 \u0939\u0940 \u0935\u093f\u0924\u0930\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u090f\u0915 \u0939\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0928\u0939\u0940\u0902\u0964<\/p>\n<p><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><strong><span style=\"color: #ff0000;\">\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f<\/span><\/strong>, \u092f\u0939 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u0939\u092e \u090f\u0915 \u0938\u0939\u091c \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902: \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u00ab\u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u091c\u094b \u090f\u0915 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0940 \u0939\u0948\u00bb \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u090f\u0915 \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u0938\u092e\u091d \u0915\u0947 \u0932\u093f\u090f, \u0907\u0938\u0915\u093e \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u092d\u0940 \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0906\u0907\u090f \u0907\u0938 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u094b \u0926\u0947\u0916\u0947\u0902:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><\/span> \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{X}<\/span><\/span> \u092a\u0930 \u090f\u0915 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:\\Omega \\longmapsto \\mathcal{X}<\/span><\/span> \u0939\u0948<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0938\u092c\u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092e\u093e\u092e\u0932\u093e \u0924\u092c \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{X}= \\mathbb{R},<\/span><\/span> \u0914\u0930 \u091c\u092c \u0924\u0915 \u0905\u0928\u094d\u092f\u0925\u093e \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e, \u0939\u092e \u0907\u0938\u0947 \u092e\u093e\u0928 \u0932\u0947\u0902\u0917\u0947; \u092f\u093e\u0928\u0940, \u0939\u092e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u092e\u093e\u0928 \u0935\u093e\u0932\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930, \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u092c\u0921\u093c\u0947 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0938\u0947 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X,Y,Z, \\cdots,<\/span><\/span>, \u091c\u092c\u0915\u093f \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u094b \u091b\u094b\u091f\u0947 \u0905\u0915\u094d\u0937\u0930\u094b\u0902 \u0938\u0947 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u0930\u0932\u0924\u093e \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u0915\u0947\u0935\u0932 \u00ab\u091a\u0930\u00bb \u0915\u0939\u0947\u0902\u0917\u0947\u0964<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0e0ff;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000000;\"><strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/span> \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f 6 \u092a\u0915\u094d\u0937\u094b\u0902 \u0935\u093e\u0932\u093e \u090f\u0915 \u092a\u093e\u0938\u093e \u0926\u094b \u092c\u093e\u0930 \u092b\u0947\u0902\u0915\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0924\u092c \u0939\u092e\u0947\u0902 \u092f\u0939 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{2d6} = \\{(\\omega_1, \\omega_2)\\;|\\; \\omega_1,\\omega_2 \\in \\{1,2,3,4,5,6\\}\\}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0938\u0947, \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=<\/span><\/span> \u00ab\u090f\u0915 \u0915\u093e \u0906\u0928\u0947 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u00bb<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y=<\/span><\/span> \u00ab\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u00bb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">=\\omega_1 + \\omega_2<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Z=<\/span><\/span> \u00ab\u0926\u0942\u0938\u0930\u0947 \u092b\u0947\u0902\u0915\u0928\u0947 \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u00bb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">= \\omega_2<\/span><\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u094d\u092f\u093e \u0939\u0948\u0902?<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #e0ffe0;\">\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e: <\/strong><\/span><strong><span style=\"color: #ff0000;\">\u090f\u0915 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f (\u092f\u093e \u00abFD\u00bb)<\/span><\/strong> \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0915\u093e \u090f\u0915 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X: \\mathbb{R} \\longmapsto \\mathbb{R}<\/span><\/span> \u0939\u0948, \u091c\u094b \u0938\u0902\u092c\u0902\u0927 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x) = P(\\{\\omega \\;|\\; X(\\omega)\\leq x\\}),<\/span><\/span> \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948, \u092f\u093e \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X\\leq x).<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0906\u092e \u0924\u094c\u0930 \u092a\u0930, \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0909\u0938\u0915\u0940 \u0938\u094d\u092a\u0937\u094d\u091f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u090f\u0915 \u0928\u092e\u0942\u0928\u093e \u0938\u094d\u0925\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span><\/span> \u092e\u0947\u0902 \u0909\u0924\u0928\u0940 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940 \u091c\u093f\u0924\u0928\u0940 \u0915\u093f \u0909\u0938\u0915\u0940 \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X<\/span><\/span> \u092e\u0947\u0902 X \u0938\u092c\u0938\u094d\u0915\u094d\u0930\u093f\u092a\u094d\u091f \u0915\u094b \u091b\u094b\u0921\u093c\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u092f\u0926\u093f \u0938\u0902\u0926\u0930\u094d\u092d \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0914\u0930 \u0915\u094b\u0908 \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u092f\u0939 \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0915\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u093e\u0930\u094d\u092f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u0939\u0948, \u0905\u0915\u094d\u0938\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim F<\/span><\/span> \u0928\u094b\u091f\u0947\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0917\u0941\u0923\u0927\u0930\u094d\u092e<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=gIKn9t1hnrw&amp;t=806s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u090f\u0915 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u0948<\/span><\/strong><\/a> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b<\/span><\/span> \u0915\u094b\u0908 \u092d\u0940 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u092e\u093e\u0928\u094d\u092f \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p style=\"text-align: justify; color: #000000;\">(a) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b \\longrightarrow [P(a\\lt X \\leq b) = F(b) - F(a)]<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(b) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b \\longrightarrow F(a) \\leq F(b),<\/span><\/span> \u092f\u093e\u0928\u0940 \u00abF \u092c\u0922\u093c \u0930\u0939\u093e \u0939\u0948\u00bb\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">(c) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to +\\infty} F(x) = 1<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to -\\infty} F(x) = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(d) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)=\\lim_{t\\to x^+}F(t) - \\lim_{t\\to x^-}F(t)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">(e) <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F(x)=\\lim_{t\\to x^+}F(t)<\/span><\/span><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td style=\"background-color: #ffe0e0;\"><span class=\"collapseomatic \" id=\"id69e42d4bd36ee\"  tabindex=\"0\" title=\"\u092a\u094d\u0930\u092e\u093e\u0923\"    >\u092a\u094d\u0930\u092e\u093e\u0923<\/span><div id=\"target-id69e42d4bd36ee\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify; color: #000000;\"><strong>(a)<\/strong> \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u0918\u091f\u0928\u093e\u090f\u0902 \u0939\u0948\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{X\\leq a\\}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{X\\leq b\\}<\/span><\/span> \u0915\u094d\u0930\u092e\u0936\u0903, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925\u0964 \u092f\u0926\u093f \u092f\u0939 \u0938\u092c \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span><\/span> \u0914\u0930 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{P(a\\lt X\\leq b)} = P(B\\setminus A) = P(B) - P(B\\cap A) = P(B)-P(A) =\\color{blue}{F(b) - F(a)}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(b)<\/strong> \u092d\u093e\u0917 (a) \u0938\u0947 \u092f\u0939 \u0928\u093f\u0915\u093e\u0932\u093e \u0917\u092f\u093e \u0939\u0948: \u091a\u0942\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A)\\geq 0,<\/span><\/span> \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(b) - F(a) \\geq 0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u091c\u094b \u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a) \\leq F(b)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(c)<\/strong> \u092f\u0939\u093e\u0901 \u0939\u092e \u0907\u0938 \u0924\u0925\u094d\u092f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u092c\u0922\u093c\u0924\u093e \u0939\u0948 (\u092d\u093e\u0917 (b) \u092e\u0947\u0902 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0917\u092f\u093e) \u0914\u0930 \u00ab1\u00bb \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0940\u092e\u093f\u0924 \u0939\u0948 (\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u093f\u0924\u0930\u0923 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948)\u0964 \u0915\u0947\u0935\u0932 \u0907\u0938\u0938\u0947 \u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty} F(x) = 1<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0915\u093e \u092a\u0942\u0930\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0939\u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0947 \u0938\u093e\u0925 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u0928\u093e\u090f\u0902 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_n=\\{\\omega\\;|\\;X(\\omega)\\leq n\\}.<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u0938\u0947 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u0948 \u0915\u093f, \u0939\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u0939\u094b\u0917\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_{n}\\subseteq A_{n+1},<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\bigcup_{n\\lt +\\infty} A_n = \\Omega<\/span><\/span> \u0914\u0930 \u0907\u0938\u0932\u093f\u090f, <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%86%d8%b8%d8%b1%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%81%d9%8a%d8%af%d8%a9-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d8%a7%d8%aa\/\" rel=\"noopener\" target=\"_blank\">\u0938\u0924\u0924\u0924\u093e \u0938\u0902\u092a\u0924\u094d\u0924\u093f<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1=P(\\Omega) = P\\left( \\ bigcup_{n\\lt +\\infty} A_n \\right) = \\lim_{n\\to +\\infty} P(A_n) = \\lim_{n\\to +\\infty} P(\\{\\omega\\;|\\;X(\\omega)\\leq n\\}) = \\lim_{n\\to +\\infty} P(X\\leq n)=\\lim_{n\\to +\\infty}F(n)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0905\u0930\u094d\u0925\u093e\u0924:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\lim_{x\\to +\\infty} F(x) = 1}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924, \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to -\\infty<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092a\u0939\u0932\u0947 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B_n=\\{\\omega\\;|\\;-n\\lt X(\\omega)\\}.<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u0938\u0947 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{n \\ to -\\infty}F(n) = \\lim_{n\\to -\\infty} P(X\\leq n) = \\lim_{n\\to \\infty} P(X\\leq -n)= 1 - \\lim_{n\\to \\infty} P(-n \\lt X) = 1 - \\lim_{n\\to \\infty}P(B_n)) = 1 - P(\\Omega) = 1-1=0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(d)<\/strong> \u0907\u0938\u0947 \u092d\u093e\u0917 (c) \u0915\u0940 \u0924\u0930\u0939 \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0938\u0947\u091f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle C_n = \\left\\{x - \\frac{1}{n} \\leq X \\leq x + \\frac{1}{n}\\right\\}<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0915\u0947 \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> C_{n+1}\\subseteq C_n<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcap_{n\\gt 0} C_n = \\{X=x\\}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0932\u093f\u090f, <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%86%d8%b8%d8%b1%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%81%d9%8a%d8%af%d8%a9-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d8%a7%d8%aa\/\" rel=\"noopener\" target=\"_blank\">\u0938\u0924\u0924\u0924\u093e \u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u093e \u090f\u0915 \u092a\u0930\u093f\u0923\u093e\u092e<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)=P\\left(\\bigcap_{n\\gt 0} C_n \\right) = \\lim_{n\\to \\infty} P(C_n) = \\lim_{x+1\/n \\ to x^+}F\\left(x+1\/n\\right) - \\lim_{x-1\/n \\to x^-}F\\left(x-1\/n\\right)= \\lim_{t \\ to x^+}F\\left(t\\right) - \\lim_{t \\to x^-}F\\left(t\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>(e)<\/strong> \u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u092e\u093e\u092e\u0932\u093e \u092a\u093f\u091b\u0932\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u091a\u0942\u0902\u0915\u093f \u0939\u092e\u0928\u0947 \u092a\u0939\u0932\u0947 \u0939\u0940 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930 \u0926\u093f\u092f\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X=x)= \\lim_{t \\ to x^+}F\\left(t\\right) - \\lim_{t \\ to x^-}F\\left(t\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0939\u092e \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{t \\ to x^+}F\\left(t\\right) = P(X=x) + \\lim_{t \\ to x^-}F\\left(t\\right) = P(X=x) + \\lim_{t\\to x^-}P(X\\leq t)= P(X\\leq x) = F(x)<\/span><\/span><\/p>\n<\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u0910\u0938\u093e \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0926\u094b \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y<\/span><\/span> \u0915\u093e \u0938\u092e\u093e\u0928 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0939\u094b\u0924\u093e \u0939\u0948 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall A\\subseteq \\mathbb{R})(P(X\\in A) = P(Y\\in A)).<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u090f\u0915 \u0939\u0940 \u0928\u092e\u0942\u0928\u093e \u0938\u094d\u0925\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span><\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0926\u094b \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y<\/span><\/span> \u0938\u092e\u093e\u0928 \u0935\u093f\u0924\u0930\u0923 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u0932\u093f\u090f \u0935\u0947 \u091c\u0930\u0942\u0930\u0940 \u0928\u0939\u0940\u0902 \u0915\u093f \u090f\u0915 \u0939\u0940 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0939\u094b\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0939\u092e \u090f\u0915 \u0938\u0902\u0924\u0941\u0932\u093f\u0924 \u0938\u093f\u0915\u094d\u0915\u0947 \u0915\u0947 \u092b\u0947\u0902\u0915\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u092e\u093e\u0928\u0947\u0902 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=1<\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u094b \u0939\u0947\u0921\u094d\u0938 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X=0<\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u094b \u091f\u0947\u0932\u094d\u0938, \u0939\u092e \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Y=1-X<\/span><\/span> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X=1) = P(Y=1)=0.5,<\/span><\/span> \u0914\u0930 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u0928 \u0935\u093f\u0924\u0930\u0923 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092f\u0926\u093f \u0939\u092e \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u0928 \u092e\u093e\u0928 \u0939\u094b\u0928\u0947 \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e \u0915\u094d\u092f\u093e \u0939\u0948, \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0917\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X=Y)=0<\/span><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0938\u093e\u0930\u093e\u0902\u0936\u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 \u0915\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u092e\u0947\u0902 \u0917\u0939\u0928\u0924\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948, \u091c\u094b \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0914\u0930 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0938\u094d\u0924\u0902\u092d \u0939\u0948\u0902\u0964 \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0915\u094b \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u094b \u090f\u0915 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26787,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[577,678],"tags":[],"class_list":["post-26803","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-678"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0930\u0948\u0916\u093f\u0915 \u091a\u0930 \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0935\u093f\u0924\u0930\u0923 - 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