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4.5: Sura ya Mapitio ya Mfumo

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    180042

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    Hypergeometric usambazaji

    \(h(x)=\frac{\left(\begin{array}{l}{A} \\ {x}\end{array}\right)\left(\begin{array}{l}{N-A} \\ {n-x}\end{array}\right)}{\left(\begin{array}{l}{N} \\ {n}\end{array}\right)}\)

    Usambazaji wa Binomial

    \(X \sim B(n, p)\)ina maana kwamba kipekee random variable\(X\) ina binomial uwezekano usambazaji na\(n\) majaribio na uwezekano wa mafanikio\(p\).

    \(X =\)idadi ya mafanikio katika majaribio ya kujitegemea

    \(n =\)idadi ya majaribio ya kujitegemea

    \(X\)inachukua maadili\(x = 0, 1, 2, 3, ..., n\)

    \(p =\)uwezekano wa mafanikio kwa jaribio lolote

    \(q =\)uwezekano wa kushindwa kwa jaribio lolote

    \(p + q = 1\)

    \(q = 1 – p\)

    Maana ya\(X\) ni\(\mu = np\). kupotoka kiwango cha\(X\) ni\(\sigma=\sqrt{n p q}\).

    \[P(x)=\frac{n !}{x !(n-x) !} \cdot p^{x} q^{(n-x)}\nonumber\]

    \(P(X)\)wapi uwezekano wa\(X\) mafanikio katika\(n\) majaribio wakati uwezekano wa mafanikio katika yoyote TRIAL ONE ni\(p\).

    Usambazaji wa Jiometri

    \(P(X=x)=p(1-p)^{x-1}\)

    \(X \sim G(p)\)ina maana kwamba discrete random variable\(X\) ina kijiometri uwezekano usambazaji na uwezekano wa mafanikio katika kesi moja\(p\).

    \(X =\)idadi ya majaribio ya kujitegemea mpaka mafanikio ya kwanza

    \(X\)inachukua maadili\(x = 1, 2, 3, ...\)

    \(p =\)uwezekano wa mafanikio kwa jaribio lolote

    \(q =\)uwezekano wa kushindwa kwa jaribio lolote\(p + q = 1\)
    \(q = 1 – p\)

    Maana ni\(\mu = \frac{1}{p}\).

    Kupotoka kwa kiwango ni\(\sigma=\sqrt{\frac{1-p}{p^{2}}}=\sqrt{\frac{1}{p}\left(\frac{1}{p}-1\right)}\).

    Poisson Usambazaji

    \(X \sim P(\mu )\)ina maana kwamba\(X\) ina Poisson uwezekano usambazaji ambapo idadi\(X =\) ya matukio katika kipindi cha riba.

    \(X\)inachukua maadili\(x = 0, 1, 2, 3, ...\)

    maana\(\mu\) au\(\lambda\) ni kawaida kutolewa.

    ugomvi ni\(\sigma ^2 = \mu\), na kupotoka kiwango ni
    \(\sigma=\sqrt{\mu}\).

    Wakati\(P(\mu)\) hutumiwa kwa takriban usambazaji wa binomial,\(\mu = np\) ambapo n inawakilisha idadi ya majaribio ya kujitegemea na\(p\) inawakilisha uwezekano wa kufanikiwa katika jaribio moja.

    \[P(x)=\frac{\mu^{x} e^{-\mu}}{x !}\nonumber\]