STAT 5100 Midterm: STAT 5100 Iowa Midterm2c
Document Summary
Please write your answers in the exam books provided. You can use formulas from page 2 when appropriate: (5 points) let x, y , and z be independent random variables with means and variances. Let u = xz and v = y z. Find the covariance of u and v : (5 points) let x have density f (x) = 1. Find the mean and variance of x: (5 points) suppose x and y are independent continuous non-negative random variables with densities fx(x) =(2xe x2. 0 for x > 0 otherwise fy (y) =(e y. Find the density of u = x 2/y : (5 points) let p have a distribution on [0, 1] with density f (p) = 3p2. The conditional distribution of x given p = p is geometric(p), with possible values. 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.
