See question attached - will give fast feedback! Thank you

Problem 4. Let S = (31,82) be a point uniformly distributed in the disk of radius 1 centered at the origin (so (5'1, 32) is the Euclidean coordinates for the point 8'), and let X, Y be independent standard normal variables. (a) Let W = 81X + 821/. Find the variance of W. (b) Com ute IF'(\\/X2 + Y2 s S2 + 82). P 1 2