Statistical Sciences 2141A/B Lecture Notes - Lecture 20: Normal Distribution, Chi Distribution, Gamma Distribution

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

If a rv x has a standard normal distribution, then the rv y = x2 is said to have a "chi-square distribution with one degree of freedom" Mo(cid:396)e gene(cid:396)ally, if a se(cid:395)uence of independent (cid:396)(cid:448)"s xi ~ n(cid:894)(cid:1004), (cid:1005)(cid:895) (cid:449)he(cid:396)e (cid:1004) i v, then the rv is said to have a chi-square distribution with v degrees of freedom. "degrees of freedom is related to our sample size. When we look at hypothesis testing and stuff like that, we will get more specific. For now, remember it as the number of normal variables that you need" This is denoted by y ~ xv2 and critical values are denoted by. A chi-square distribution with v degrees of freedom is a gamma distribution with parameters k = v/2 and = (cid:1005)/(cid:1006) The expected value and variance are v and 2v respectively. Values for the chi distribution can be found in the t tables on the owl (cid:894)student"s(cid:895) t-distribution.