Statistics 310/732 Assignment 3 Due:00pm, May 10, 2017 1 A Discrete Multivariate Probability Distribution. In the following we will investigate a...

having problem with question 3

Consider the function fX,Y (x, y) = 1 2π e − 1 2 (x 2+y 2 ) 1 + xye− 1 2 (x 2+y 2 ) . Show that each of the marginal distributions for X and Y are standard Normal distributions but X and Y are not independent of each other. Hint: You need only find the marginal distribution of one of these variables — you using symmetry arguments for the other. Note: that as its marginal distributions are p.d.fs than we can conclude that the function fX,Y (x, y) is now p.d.f.