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A contractor is required by a county planning department
Chapter 4, Problem 14E(choose chapter or problem)
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: \(\sum _{v=1} ^5 \ \rho(y)=1\).]
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 \(fp(y) = y^2 / 50\) for y = 1…….,5 be the pmf of Y?
Questions & Answers
QUESTION:
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: \(\sum _{v=1} ^5 \ \rho(y)=1\).]
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 \(fp(y) = y^2 / 50\) for y = 1…….,5 be the pmf of Y?
ANSWER: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