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Question
Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).
Solution
X ~ B(n, p)
Given: n = 10 and E(X) = 5
But E(X) = np ∴ np = 5
∴ 10p = 5
∴ p = `1/2`
∴ q = 1 - p = `1 - 1/2 = 1/2`
Var(X) = npq = `10(1/2)(1/2) = 2.5`
Hence, p = `1/2` and Var(X) = 2.5
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