If the standard deviation of the random variable X is 3 p q and mean is 3p then E x 2 = … .

Step-by-step solution

Key Idea: Use p +q =1 and V a r X = E X 2 - E X 2 We have standard deviation of X = 3 p q ⇒ V a r X = 3 p q and mean, E X = 3 p Now, 3 p q = E x 2 - 3 p 2 ∵ V a r X = E X 2 - E X 2 ⇒ E X 2 = 3 p q + 9 p 2 = 3 p 1 - p + 9 p 2 ∵ p + q = 1 = 3 p - 3 p 2 + 9 p 2 ⇒ 3 p + 6 p 2 ⇒ 3 p 1 + 2 p