A contractor is required by Hampshire county planning depart

A contractor is required by Hampshire 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. What is the value of k? What is the probability that at most three forms are required? What is the probability that between two and four forms (inclusive) are required?

Solution

P(Y) = KY FOR ALL Y =1 TO 5

ALSO PROBABILITY IS 1 FOR ALL Y

THEREFORE K+2K+3K+4K+5K= 1 ( AS P(Y) = KY)

THEREFORE K =1/15 = 0.066

B) AT MOST THREE FORMS ARE REQUIRED

P(Y=1) = 5C1(1/5)^1*(4/5)^4

p(Y=2)= 5C2(2/5)^2*(3/5)^3

p(Y=3)= 5C3(3/5)^3*(2/5)^2

C) SIMILARLY WE CAN FIND AS WE DID IN LAST PART FOR Y = 2, Y=3 ,Y=4