STAT 100A Lecture Notes - Lecture 18: Cumulative Distribution Function, Random Variable
Document Summary
De nition normal random variable if its probability density function is (normal random variable). A random variable x is said to be a f(x) = 2 2 e where and 2 are parameters. 2 = 1 then x is said to be a standard normal random variable. The cumulative distribution function of a standard normal x is denoted by (x). Let x be a standard normal random variable. Theorem ax + b where a > 0 is normally distributed with parameters a + b and a2 2. If x is normally distributed with parameters and 2, then y = = p(ax + b y) a (cid:3) = p(cid:2)x y b a (cid:3) 1 a f x(cid:2) y b a (cid:3) Theorem is normally distributed with parameters 0 and 1. If x is normally distributed with parameters and 2, then z = x . Let x be a normal random variable with parameters.
