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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,\(p\left( y \right) = ky\)for\(y = 1, \ldots ,5\).

a. What is the value of k? (Hint:\(\sum\limits_{y = 1}^5 {p\left( y \right)} = 1\))

b. What is the probability that at most three forms arerequired?

c. What is the probability that between two and fourforms (inclusive) are required?

d. Could \(p\left( y \right) = \frac{{{y^2}}}{{50}}\)for \(y = 1, \ldots ,5\)be the pmf of Y?

Step by step solution

01

Step 1

It is given that,the probability that y forms are required is known to be proportional to y is\(p\left( y \right) = ky\,\,\,{\rm{for}}\,y = 1,2,3, \ldots ,5\). The total number of forms in applying the building submit is 5.

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