Question

A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) in applying for a building permit. Let $y$ be 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, $p(y)=k y$ for $y=1, \ldots, 5$. a. What is the value of $k ?$ (Hint: $\Sigma p(y)=1 .$ ) 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 $p(y)=y^{2} / 50$ for $y=1,2,3,4,5$ be the probability distribution of $y$ ? Explain.

          A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) in applying for a building permit. Let $y$ be 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, $p(y)=k y$ for $y=1, \ldots, 5$.
a. What is the value of $k ?$ (Hint: $\Sigma p(y)=1 .$ )
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 $p(y)=y^{2} / 50$ for $y=1,2,3,4,5$ be the probability distribution of $y$ ? Explain.

Added by Soledad V.

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