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Given X~B(n,p) if E(X) = 6, Var (X) = 4....

Given `X~B(n,p)` if E(X) = 6, Var (X) = 4.2 , find the value of n and p.

Text Solution

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`E (X) = 6 , Var (X) = 4.2 , E (X) = np `
` Var (X) = npq `
`therefore ("Var(X)")/(E(X)) = ("npq)/(np) = q = (4.2) /(6) = 0.7`
` q = 0.7 `
Since given function is a binomial function
` therefore p = 1 - q = 1 - 0.7 = 0.3 `
Now , np = 6
` therefore n = (6)/(p) = (6)/(0.3) = 20 ` .
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