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 defective tires.
a. If X and Y are independent with pX(0) =.5, pX(1) =.3, pX(2) = .2, and pY(0) = .6, pY(1) =.1, pY(2) = pY(3) = .05, and pY (4) = .2, display the joint pmf of (X, Y) in a joint probability table.
b. Compute P(X ≤ 1 and Y ≤ 1) from the joint probability table, and verify that it equals the product P(X ≤ 1) . P(Y ≤ 1).
c. What is P(X + Y = 0) (the probability of no violations)?
d. Compute P(X + Y ≤ 1).
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