{"id":34356,"date":"2021-07-07T13:00:20","date_gmt":"2021-07-07T13:00:20","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34356"},"modified":"2025-09-07T23:25:01","modified_gmt":"2025-09-07T23:25:01","slug":"distributiones-discretae-probabilitatis-et-exempla","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/distributiones-discretae-probabilitatis-et-exempla\/","title":{"rendered":"Distributiones Discretae Probabilitatis et Exempla"},"content":{"rendered":"
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Distributiones Discretae Probabilitatis et Exempla<\/h1>\n

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\n Summarium<\/strong>
\n In hac lectione penitus investigabimus distributiones discretas probabilitatis, incipientes a definitione earum ex spatiis exemplorum continuis et discretis. Exhibebuntur quinque distributiones discretae probabilitatis notissimae: Binomialis sive Bernoulliana, Poissoniana, Geometrica, Binomialis Negativa et Hypergeometrica, unaquaeque cum exemplis quae applicationem earum in rebus vitae cotidianae demonstrant. Praeterea proponuntur exercitationes quae usum harum distributionum in condicionibus practicis comprehendunt, ut in ludis chartarum et venditione productorum, studentibus praebentes intellectum adhibitum harum instrumentorum essentialium statisticae.<\/em>\n <\/p>\n

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\n OBJECTIVA DISCENDI:<\/strong> Ad finem huius lectionis, studiosus poterit:\n <\/p>\n

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  1. Intellegere<\/strong> notionem distributionis discretae probabilitatis eiusque notas praecipuas.<\/li>\n
  2. Applicare<\/strong> distributionem binomialem, Poissonianam, geometricam, binomialem negativam et hypergeometricam.<\/li>\n<\/ol>\n


    \n INDEX CONTENTORUM<\/u>:<\/strong>
    \n
    \n Notio distributionis discretae probabilitatis<\/strong><\/a>
    \n     Quinque Distributiones discretae probabilitatis notissimae<\/strong><\/a>
    \n     Binomialis sive Bernoulliana<\/a>
    \n     Distributio Poissoniana<\/a>
    \n     Geometrica<\/a>
    \n     Binomialis Negativa<\/a>
    \n     Hypergeometrica<\/a>
    \n     Exercitationes Propositae<\/strong><\/a>
    \n <\/center>\n<\/div>\n

    Cum studemus spatia exemplorum<\/a>, animadvertimus haec duo genera habere posse: discreta et continua. Cum spatium exemplorum continuum est, fieri potest definire variabiles aleatorias huius naturae atque ex his statuere distributiones discretas probabilitatis. Iam recensuimus quae ad variabiles aleatorias pertinent hic<\/a>, nunc nos conferemus in distributiones discretas probabilitatis.<\/p>\n

    <\/a><\/p>\n

    Notio distributionis discretae probabilitatis<\/h2>\n

    Dicimus variabilem aleatoriam X<\/span><\/span> distributionem discretam probabilitatis habere si exstat collectio C\\subset\\mathbb{R}<\/span><\/span> finita vel infinita numerabilis talis ut P\\left(X\\in C\\right)=1;<\/span><\/span> hoc modo, si habemus valores x\\in C<\/span><\/span> tales ut p_X(x) = P(X=x),<\/span><\/span> verificari potest quod si A\\subset\\mathbb{R},<\/span><\/span> tum:<\/p>\n

    \\begin{array}{lr}\n\n(*) & P\\left(X\\in A\\right) = \\displaystyle \\sum_{x\\in A \\cap C} p_X(x)\n\n\\end{array}<\/span><\/span><\/p>\n

    Et in specie,<\/p>\n

    \\begin{array}{lr}\n\n(**) & \\displaystyle \\sum_{x\\in C} p_X(x) = 1.\n\n\\end{array}<\/span><\/span><\/p>\n

    Si computamus P(X\\in A)<\/span><\/span> utens A=]-\\infty, t],<\/span><\/span> invenimus quod:<\/p>\n

    P(X\\in A) = P(X\\leq t) = F_X(t) = \\displaystyle \\sum_{x\\leq t}p_X(x)<\/span><\/span><\/p>\n

    Ex hoc calculo concludimus F_X<\/span><\/span> esse \u00abscalam\u00bb cum saltibus in x\\in C<\/span><\/span> magnitudinis p_X(x).<\/span><\/span> Functio p_X<\/span><\/span> quae it ex C<\/span><\/span> in [0,1]<\/span><\/span> est quod appellamus functio frequentiarum<\/strong>. Ita distributio discreta datur per collectionem finitam vel infinitam numerabilem C\\subset \\mathbb{R}<\/span><\/span> et functionem p_X(x)\\geq 0<\/span><\/span> definitam pro quolibet x\\in C<\/span><\/span> quae satisfacit expressionibus (*) et (**).<\/p>\n

    <\/a><\/p>\n

    Quinque distributiones discretae probabilitatis notissimae<\/h2>\n


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