Question

Given that X ~ B(n,p), if n = 25, E(X) = 10, find p and Var (X).

Answer 1

X ~ B(n,p)
Here, n = 25, E(X) = 10
∴ np = 10

∴ p = `(10)/"n" = (10)/(25) = (2)/(5)`

∴ q = 1 – p = `1 - (2)/(5) = (3)/(5)`

∴ Var(X) = npq

= `25 xx (2)/(5) xx (3)/(5)`

= 2 x 3
= 6.