Question

Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).

Answer 1

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