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Question
Solve the following problem :
Let X∼B(n,p) If n = 10 and E(X)= 5, find p and Var(X).
Solution
Let X ~ B(n, p)
n = 10, E(X) = 5 ...[Given]
But E(X) = np
∴ 5 = 10(p)
∴ p = `(1)/(2)`
∴ q = 1 – p = `1 - (1)/(2) = (1)/(2)`
Var (X) = npq
= `10 xx (1)/(2) xx (1)/(2)`
= `1 xx (1)/(4)`
= 2.5
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