Problem 6 The bivariate normal distribution is frequently assumed to describe the impact points of rounds red at a target in a twodimensional plane. That is, if we imagine an (3:, y) coordinate system centered at the target, the vertical miss distance is Y and the horizontal miss distance is X. Assume that (X , Y) are bivariate normal with pix = 0.2, [.LY = 0.2, ox = 0.4, CY = 4 and correlation p = 0.3. (a) Compute IP(X S 0.4) and IP(|Y| g 0.4). (b) Compute lP(X > 0|Y = 0.2), the probability that the round hits to the right of the target, given that it was 0.2 units below the target. (c) Compute 1P(X 2 + Y2