A civil engineer is studying a left-turn lane that is long enough to hold 7 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 prob. that X = x is proportional to (x + 1)(8 - x) for  x = 0, 1, . . . ,7

a) Find the probability mass function of X.

b) Find the probability that X will be at least 5.

http://www.bilkent.edu.tr/~math250/Solution%20set2.pdf