EL ENG 126 Study Guide - Midterm Guide: Normal Distribution, Dey
Document Summary
Department of eecs - university of california at berkeley. Eecs 126 - probability and random processes - spring 2007. X is uniformly distributed in [0, 1] and y is ex- ponentially distributed with mean 1, so that p (y > y) = e y for y 0. Calculate the mean and the variance of z. Hint: you may need the following intermediate results. Nds that a0 = 1 e 1, a1 = 1 2e 1, a2 = 2 5e 1, a3 = 6 16e 1. We have p (z > x) = p (x > x, y > x) = p (x > x)p (y > x) = (1 x)e x for x [0, 1]. The density fz of z is thus given by fz(x) = d dx. P (z > x) = e x + (1 x)e x = 2e x xe x, for 0 x 1.
