11. Building contractors are required by a county planning department to submit two, three, four, five, or six forms, depending on the nature of the project, when applying for a building permit. Let Y = number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y. Thus, P(Y = y) = ky for y = 2, 3, 4, 5, 6 and k > 0. (a) Find the value of k so that P(Y = y) = ky is a PDF. (PDF's are discussed in your book.) Answer: 1/20 (b) What is the probability that at most four forms are required of the next applicant? Answer: 9/20 (c) What is the probability that between two and five forms, inclusive, are required of the next applicant? Answer: 0.7 (d) Construct a histogram for this PDF. (4.1.4)