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Question
Given that X ~ B(n,p), if n = 10, E(X) = 8, find Var(X).
Solution
X ~ B(n,p)
Here, n = 10, E(X) = 8
∴ np = 8
∴ p = `(8)/"n" = (8)/(10) = (4)/(5)`
∴ q = 1 – p = `1 - (4)/(5) = (1)/(5)`
∴ Var(X) = npq
= `10 xx (4)/(5) xx (1)/(5)`
= `2 xx (4)/(5)`
= `(8)/(5)`
= 1.6
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