low a Poisson distribution with a mean of 20 calls per minute. (a) What is the mean time until the one-hundredth call? (b) What is the mean time between calls number 60 and 80? (c) What is the probability that three or more calls occur within

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Q.4-118
aid vilidedor9 bns 2oldainsV mobns auounitno Exercises
147
4-118. Calls to the helpline of a large computer distributor fol-
low a Poisson distribution with a mean of 20 calls per minute.
(a) What is the mean time until the one-hundredth call?
(b) What is the mean time between calls number 60 and 80?
(c) What is the probability that three or more calls occur within
bas 15 seconds?
4-119. The time between arrivals of customers at an auto-
matic teller machine is an exponential random variable with a
mean of five minutes.
(a) What is the probability that more than two customers arrive
in 10 minutes?
(b) What is the probability that the time until the fifth customer
883D6 bns
arrives is less than 15 minutes?
4-120. Use integration by parts to show that T(r) = (r – 1)
r(r - 1).
w ni) Insnoqmoo s lo omitslil orls
4-121. Show that the gamma density function f(x, ^, r) inte-
grates to 1.
4-122 Use the result for the gamma distribution to determine the
mean and variance of a chi-square distribution with r=7/2.
4-123. Patients arrive at a hospital emergency department
according to a Poisson process with a mean of 6.5
(a) What is the mean time until the 10th arrival?
(d) bns (8) 2neg ai g
per
hour.
(b) What is the probability that more than 20 minutes is
required for the third arrival?
4-124. The total service time of a multistep manufacturing
operation has a gamma distribution with mean 18 minutes and
standard deviation 6.
(a) Determine the parameters 2 and r of the distribution.
Transcribed Image Text:aid vilidedor9 bns 2oldainsV mobns auounitno Exercises 147 4-118. Calls to the helpline of a large computer distributor fol- low a Poisson distribution with a mean of 20 calls per minute. (a) What is the mean time until the one-hundredth call? (b) What is the mean time between calls number 60 and 80? (c) What is the probability that three or more calls occur within bas 15 seconds? 4-119. The time between arrivals of customers at an auto- matic teller machine is an exponential random variable with a mean of five minutes. (a) What is the probability that more than two customers arrive in 10 minutes? (b) What is the probability that the time until the fifth customer 883D6 bns arrives is less than 15 minutes? 4-120. Use integration by parts to show that T(r) = (r – 1) r(r - 1). w ni) Insnoqmoo s lo omitslil orls 4-121. Show that the gamma density function f(x, ^, r) inte- grates to 1. 4-122 Use the result for the gamma distribution to determine the mean and variance of a chi-square distribution with r=7/2. 4-123. Patients arrive at a hospital emergency department according to a Poisson process with a mean of 6.5 (a) What is the mean time until the 10th arrival? (d) bns (8) 2neg ai g per hour. (b) What is the probability that more than 20 minutes is required for the third arrival? 4-124. The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6. (a) Determine the parameters 2 and r of the distribution.
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