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Given X ~ B(N, P). If N = 20, E(X) = 10, Find P, Var. (X) and S.D. (X). - Mathematics and Statistics

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Given X ~ B(n, p). If n = 20, E(X) = 10, find p, Var. (X) and   S.D. (X).

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Solution

n = 20, E(X) = 10,

`E(x)=np`

`p=(E(x))/n`

`p=1/2`

`p=1-q`

`q=1/2`

`Var(x)=npq`

`=20 xx 1/2 xx 1/2`

`=5`

`S.D. (X)=sqrt(Var(x))`

`=sqrt5`

Concept: Bernoulli Trial - Normal Distribution (P.D.F)
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