A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature of the project) in applying for a building permit. Let Y 5 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) 5 ky for y 5 1, . . . , 5.
a. What is the value of k? [Hint: ∑5Y = 1 P (Y) = 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 p(y) = y2/50 for y 1,..., 5 be the pmf of Y?