Problem 1. A civil engineer is studying a left-turn lane that is long enough to hold seven cars. Let X be the number of cars in the lane at the end of a randomly chosen red light. The engineer believes that the probability that X = x is proportional to (x + 1)(8− x) for x = 0, 1, ..., 7. (A) Find the PMF of X. (B) Find the probability that X is at least five.

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