# Normal Random Variables Question

by Onetimeuser
Tags: normal, random, variables
 HW Helper P: 1,361 For a normally distributed random variable, $$P(a < X < b) = P(X < b) - P(X < a)$$ For any random variable $W$, if $a, b$ are real numbers, and $$Z = aW + b$$ then $$E(Z) = aE(W) + b, \quad Var(Z) = a^2 Var(W)$$ (as long as the mean and variance of $W$ exist)