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.? hat is the value of k? [Hint: .] b.?? hat 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?

Answer Step 1 of 4 a) p(y) = ky for y=1,….,5. P(1)= k1 P(1)= k2 P(1)= k3 P(1)= k4 P(1)= k5 Total probability=1 k+2k+3k+4k+5k=1 15k=1 k=1/15 The probability distribution is x 1 2 3 4 5 P(x) 1/15 2/15 3/15 4/15 5/15 Step 2 of 4 b) P(at most three forms are required)=P(x3) =1/15+2/15+3/15 =6/15