STAT 4105 Study Guide - Midterm Guide: Poisson Distribution

• School: Virginia Tech
• Department: Statistics
• Course: STAT 4105
• Professor: JP Morgan

Document Summary

2 = v ar[y ] = n(cid:18) r. N (cid:19)(cid:18) n n p(y) = (cid:0)r y(cid:1)(cid:0)n r n y(cid:1) (cid:0)n n(cid:1: n = the size of the population, n = the size of the sample, r = the number of successes in the population. Find moments by di erentiating with respect to t and setting t = 0. F (y) = z y f (y)dy f (y) = V ar[y ] = e[y 2] (e[y ])2. = e[y ] = a + b. 2 = v ar[y ] = (b a)2. Standard normal: n ( = 0, = 1) 2 = v ar[y ] = 2. 4. 7 beta distribution f (y) = y 1(1 y) 1. 2 = v ar[y ] = ( + )2( + + 1) 4. 9 other expected values m(t) = e[ety ] = z etyf (y)dy.