MTH 304 Study Guide - Independent And Identically Distributed Random Variables

• School: Ryerson University
• Department: Mathematics
• Course: MTH 304
• Professor: Elizabeth Carlson

Document Summary

Table of common distributions taken from statistical inference by casella and berger. Discrete distrbutions mean p variance p(1 p) mgf/moment (1 p) + pet n np. 1 p n ( + )2 np(1 p) (n +1)(n 1) Beta-binomial(n; ; ) pmf px(1 p)1 x; x = 0; 1; p 2 (0; 1) (n. Geometric(p) x)px(1 p)n x; x = 1; : : : ; n ( n. N ; x = 1; : : : ; n p(1 p)x 1; p 2 (0; 1) Notes: if xjp is binomial (n; p ) and p is beta( ; ), then x is beta-binomial(n; ; ). Note: y = x 1 is negative binomial(1; p). The distribution is memoryless: p (x > sjx > t) = p (x > s t). ; x = 1; : : : ; k x )( n m. M (n k) x m; n; m; k > 0.