Let us consider a random variable Q whose probability distribution function is pQ(n) = ne^n for all integers n 0, and pQ(x) = 0 if x / {0, 1, . . . , }.

1. Compute .

2. Compute P(Q > 3).

3. Assume that we conduct an experiment and monitor the number of cars waiting to enter highways (in some interval of time), and that this number is a random variable with the same probability distribution function as Q. Assume that we monitor 15 such independent highways and that a highway is considered to be fluid if the number of cars waiting to enter is at most 3. Compute the probability that exactly 14 highways are fluid.