Question

If X∼B (n, p) with n = 10, p = 0.4 then E(X²) = ______.

Options

• 4

• 2.4

• 3.6

• 18.4

Answer 1

If X∼B (n, p) with n = 10, p = 0.4 then E(X²) = 18.4.

Explanation:

n = 10, p = 0.4, q = 0.6

∵ E(x) = np = 4

and V(x) = npq = 10(0.4)(0.6) = 2.4

Now, V(x) = E(x²) – [E(x)]²

`\implies` 2.4 = E(x²) – (4)²

 `\implies` E(x²) = 18.4