A contractor is required by a county planning department to submit one, two, three, four...

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 =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 fp(y) = y² /50 for y = 1…….,5 be the pmf of Y?