Question

Solve the following problem :

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

Answer 1

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