Question

Solve the following problem :

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

Answer 1

Let X ~ B(n, p)
E(X) = 5 and Var (X) = 2.5      …[Given]
But E(X) = np = 5 and
Var (X) = npq = 2.5
∴ 5(q) = 2.5

∴ q = `(2.5)/(5) = (1)/(2)`

∴ p = 1 – q = `1 - (1)/(2) = (1)/(2)`

Now, np = 5

∴ `"n"(1/2)` = 5

∴ n = 10.