Random variable

Question

Let X be the random variable with mean μ and standard deviation σ>0 and X*=(x-μ) /σ.

Then Var(X*) is

A. σ

B. σ²

C. √σ

D. 1

Answer 1

Variance of r.v, X (normal random variable) is σ², and the variance of

X*=(x-μ) /σ is 1 (X* is standard normal random variable).

 

Answer 2

Normal distribution: variance is σ²

so answer is B

The X* formula is that of Z scores, and therefore st. dev. = 1, so Bobosharif's answer wins.