Question

The mean and standard deviation of random variable X are 10 and 5 respectively, then `"E"(("X" - 15)/5)^2` = ______.

Options

• 4

• 3

• 2

• 5

Answer 1

The mean and standard deviation of random variable X are 10 and 5 respectively, then `"E"(("X" - 15)/5)^2` = 2.

Explanation:

Var(X) = `sigma^2 = 5^2` = 25

Var(X) = E(X²) – [E(X)]²

⇒ 25 = E(X²) – 10²

⇒ E(X²) = 125

`"E"(("X" - 15)/5)^2 = "E"(("X"^2 - 30"X" + 225)/25)`

= `1/25 ["E"("X"^2) - 30"E"("X") + 225]`

= `1/25 (125 - 300 + 225)`

= 2