STAT 5100 Midterm: STAT 5100 Iowa Midterm2a
Document Summary
Please write your answers in the exam books provided: let x gamma( , 1) and y gamma( , 1) be independent. Find the marginal density of x/y : let a = {(x, y) : 0 < x < 1, |y| < x2(1 x)}. A point (x, y ) is selected uniformly from a. (a) find the marginal density of x. Identify the distribution by name if you can. (b) find the conditional distribution, the conditional mean, and the condi- tional variance of y given x = x for 0 < x < 1. Identify the distribution by name if you can. P (x = x|p) = px(1 p)1 x; x = 0, 1; 0 p 1. Bernoulli(p) pmf mean, variance e[x] = p, var(x) = p(1 p) mgf. Poisson( ) pmf mean, variance e[x] = , var(x) = mgf. Beta( , ) pdf mean, variance e[x] = .
