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4. A contractor is required by a county planning department to submit one, two, three or four 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 = y) = k · y for y=1,2,3,4. a. What is the value of k? (Hint:?y=1? P(Y = y) = 1) b. What is the probability that at most two forms are required? (Hint: Construct the pmf of Y.) c. What is the cumulative distribution function (cdf) of Y?

          4. A contractor is required by a county planning department to submit one, two, three or four 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 = y) = k · y for y=1,2,3,4.

a. What is the value of k? (Hint:?y=1? P(Y = y) = 1)

b. What is the probability that at most two forms are required? (Hint: Construct the pmf of Y.)

c. What is the cumulative distribution function (cdf) of Y?

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4. A contractor is required by a county planning department to submit one, two, three or four 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 = y) = k · y for y=1,2,3,4.

a. What is the value of k? (Hint:?y=1? P(Y = y) = 1)

b. What is the probability that at most two forms are required? (Hint: Construct the pmf of Y.)

c. What is the cumulative distribution function (cdf) of Y?

Added by Carlos G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jacob Fry

02/16/2023

Step 1

We know that the sum of all probabilities must equal 1, so we can write the equation: $$ P(Y=1) + P(Y=2) + P(Y=3) + P(Y=4) = 1 $$ Since the probabilities are proportional to y, we can substitute ky for each probability: $$ k(1) + k(2) + k(3) + k(4) = Show more…

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A contractor is required by a county planning department to submit one, two, three or four 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 = y) = k · y for y=1,2,3,4. a. What is the value of k? (Hint:∑y=1⁴ P(Y = y) = 1) b. What is the probability that at most two forms are required? (Hint: Construct the pmf of Y.) c. What is the cumulative distribution function (cdf) of Y?

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