When an automobile 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 defective tires. If X and Y are independent with p (0) = 0.5, p,(1) = 0.3, p,(2) = 0.2, and p,(0) = 0.1. p(1) = 0.6, p,(2) = p,(3) = 0.05, p,(4) = 0.2, display the joint pmf of (X, n in a joint probability table. P(x, y) Compute P(X s 1 and Ys 1) from the joint probability table. P(X s1 and Y s 1) = Does P(X s1 and Ys 1) equal the product P(Xs 1)· P(Y s 1)? O Yes O No What is P(X + Y = 0) (the probability of no violations)? MX + Y = 0) = ( Compute P(X + Ys 1). P(X + Ys 1) =

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