A contractor is required by a county planning department to submit one, two, three, four, five, six, or seven 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,..., 7. (Enter your answers as fractions.) (a) What is the value of k? [Hint: p(y) = 1] y=1 k= (b) What is the probability that at most four forms are required? (c) What is the probability that between two and six forms (inclusive) are required? (d) Could p(y) = . for y = 1, ..., 7 be the pmf of Y? No because ·Ź p(y) = 141

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A contractor is required by a county planning department to submit one, two, three, four, five, six, or seven 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, ..., 7. (Enter your answers as fractions.)
(a) What is the value of k? [Hint:
P(y) = 1]
k=
(b) What is the probability that at most four forms are required?
(c) What is the probability that between two and six forms (inclusive) are required?
y²
(d) Could p(y) =
for y = 1, ..., 7 be the pmf of Y?
141
No
, because
p(y) =
y = 1
Transcribed Image Text:A contractor is required by a county planning department to submit one, two, three, four, five, six, or seven 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, ..., 7. (Enter your answers as fractions.) (a) What is the value of k? [Hint: P(y) = 1] k= (b) What is the probability that at most four forms are required? (c) What is the probability that between two and six forms (inclusive) are required? y² (d) Could p(y) = for y = 1, ..., 7 be the pmf of Y? 141 No , because p(y) = y = 1
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