# Question

Highway A and Highway B merge to form Highway C as shown in the figure. Engineers have studied the traffic patterns on the two merging roads and found that the number of cars per minute that travel each road can be well modeled as Poisson random variables as described below

Highway A: N = # Cars per minute,

Highway A: M = # Cars per minute,

Let K = M + N be the number of cars per minute on Highway C. Find the PMF of K PK ( k) = Pr (K= k). Is K also a Poisson random variable or does it follow some other distribution? You may assume that in any interval of time, the number of cars on Highway A and the number of cars on Highway B are independent of each other.

Highway A: N = # Cars per minute,

Highway A: M = # Cars per minute,

Let K = M + N be the number of cars per minute on Highway C. Find the PMF of K PK ( k) = Pr (K= k). Is K also a Poisson random variable or does it follow some other distribution? You may assume that in any interval of time, the number of cars on Highway A and the number of cars on Highway B are independent of each other.

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