14. A contractor is required by a county planning department to submit one, two, three, four, or ve forms (depending on the nature of the project) in applying for a building permit. Let Y  the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y that is, p(y)  ky for y  1, . . . , 5.

a. What is the value of k? [Hint: .]

b. What is the probability that at most three forms are required?

c. What is the probability that between two and four forms (inclusive) are required?

d. Could p(y)  y2/50 for y  1, . . . , 5 be the pmf of Y?