Question

If the standard deviation of the random variable X is `sqrt(3"pq")` and mean is 3p then E(x²) = _______.

Options

• 3pq + 3q²

• 3p(1 + 2p)

• 3pq + 3p²

• 3q(1 + 2q)

Answer 1

If the standard deviation of the random variable X is `sqrt(3"pq")` and mean is 3p then E(x²) = 3p(1 + 2p).

Explanation:

We have standard deviation of X = `sqrt(3"pq")`

⇒ Var(X) = 3pq

and mean, E(X) = 3p

Now, 3pq = E(x²) - (3p²)   ....(∵ Var(X) = E(X²) - (E(X)²))

⇒ E(X²) = 3pq + 9p²

= 3p(1 - p) + 9p²     ...(∵ p + q = 1)

= 3p - 3p² + 9p² 

⇒ 3p + 6p² 

⇒ 3p (1 + 2p)