Question

If X is normally distributed with zero mean and unit variance, then the expectation of x2​

Answer 1

Step-by-step explanation:

If X is normally distrubuted with zero mean and unit variance, then what is the mean and variance of X^2 equal to?

X ~ N(0, 1)

⟹X2 ~ χ2(1)

⟹μ=1 and σ2=2μ=2.

In words, this says that if X is a standard normal random variable, then X2 is distributed chi-square with one degree of freedom. The mean of X2 is the number of degrees of freedom and its variance is twice the number of degrees of freedom.