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. (Enter your answers as fractions.)
(a) What is the value of k? [Hint: sum from y=1 to 5 p(y) = 1]
k = 1/15
(b) What is the probability that at most three forms are required?
2/5
(c) What is the probability that between two and four forms (inclusive) are required?
3/5
(d) Could p(y) = y^2/56 for y = 1, ..., 5 be the pmf of Y?
No, because sum from y=1 to 5 p(y) = 56/50