Question

If X ~ B(n, p), E(X) = 12, V(X) = 4, then find n

Answer 1

As X ~ B(n, p), E(X) = np and V(X) = npq

It is given that E(X) = 12 and V(X) = 4

∴ `("V"("X"))/("E"("X")) = 4/12`

∴ `"npq"/"np" = 1/3`

∴ q = `1/3`

∴ p = 1 – q

= `1 - 1/3`

= `2/3`

∴ E(X) = np = 12

⇒ `"n" xx 2/3` = 12

⇒ n = 18