STAT 5100 Midterm: STAT 5100 Iowa Midterm2b
Document Summary
Please write your answers in the exam books provided. You can use formulas from page 2 when appropriate: let x and y have joint density f (x, y) =(c(1 + 4xy) 0 for 0 < x < 1 and 0 < y < 1 otherwise. (a) show that c = 1. 2 . (b) find the marginal density of x. (c) find cov(x, y ): let x and y be independent continuous random variables with densities fx(x) =(2xe x2. 0 for x > 0 otherwise fy (y) =(e y. Some distributions x(cid:1)px(1 p)n x; x = 0, 1, . 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. Binomial(n, p) pmf mean, variance e[x] = np, var(x) = np(1 p) mgf. Poisson( ) pmf mean, variance e[x] = , var(x) = mgf. Negative binomial(r. p) pmf mean, variance e[x] = r(1 p)
