Question

Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p.

Answer 1

X ~ B(n, p)

Given: E(X) = 5 and Var(X) = 2.5

np = 5  and npq = 2.5

∴ `"npq"/"np" = 2.5/5`

∴ q = 0.5 = `5/10 = 1/5`

∴ p = 1 - p = `1 - 1/2 = 1/2`

Substituting p = `1/2` in np = 5, we get

`"n"(1/2) = 5`

∴ n = 10

Hence, n = 10 and p = `1/2`