Answer to Question #99116 in Statistics and Probability for Nayum uddin

Question

Suppose that a random variable has the normal distribution N(6, 4). Find the
expectation of X^2, E(X^2).

Answer 1

We have $\mu=6, \sigma^2=4$

We know that $Var(X)=E(X^2)-(E(X))^2$

From that , $E(X^2)=Var(X)+(E(X))^2$

$E(X^2)=\sigma^2+\mu^2$

$=4+6^2$

$=4+36=40$