7.18 A contractor is required by a county planning department to submit anywhere from one to five forms

(depending on the nature of the project) in applying for a building permit. Let y be 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: gp1 y2 5 1.)

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 p1 y2 5 y2/50 for y  1, 2, 3, 4, 5 be the probability distribution of y? Explain.