EL ENG 126 Study Guide - Midterm Guide: Multivariate Normal Distribution, Independent And Identically Distributed Random Variables, Exponential Distribution
Document Summary
Department of eecs - university of california at berkeley. Eecs 126 - probability and random processes - spring 2007. Since x + y and x y are jointly gaussian, this implies that these random variables are independent. Consequently, x + y and (x y )2 are independent: let u = x + y, v1 = x + 2y, v2 = x z, and v = (v1, v2)t . E[u |v] = e(u vt ][e(vvt )] 1v = [3, 1]" 5 2. E[x + y |x + 2y, y z] = 6 (y z): let w1 = x + y, w2 = x + z, and w = (w1, w2)t . 2 exp{ (w1 x)2/2 (w2 x)2/2}. We know that m le[x|w = w] = argmaxxfw|x [w|x]. That is, the mle is the minimizer of g(x) = Writing that the derivative of g(x) with respect to x is equal to zero, we nd so that x = (w1 + w2)/2.
