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: g p 1 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 p 1 y2 5 y2/50 for y = 1, 2, 3, 4, 5 be the probability distribution of y? Explain.