When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defe tires. (a) If X and Y are independent with px(0) = 0.5, Px(1) = 0.3, Px(2) = 0.2, and py(0) = 0.6, py(1) = 0.2, py(2) = py(3) = 0.05, py(4) = 0.1, display the joint pmf of (X, Y) in a joint probability table. P ( x, y ) 3 0 0.5 X 0.3 X 0.025 0.025 0.1 X X 0.3 X 0.18 X 0.015 0.015 0.06 X N 0.2 LX 10.12 X 0.01 0.01 0.04 X (b) Compute P(X