Pearson eText for Probability & Statistics for Engineers and Scientists with R -- Instant Access (Pearson+)
1st Edition
ISBN: 9780137548552
Author: Michael Akritas
Publisher: PEARSON+
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6.54 Let Y₁, Y2,..., Y, be independent Poisson random variables with means 1, 2,..., An
respectively. Find the
a probability function of
Y.
b conditional probability function of Y₁, given that Y = m.
Y₁ = m.
c conditional probability function of Y₁+Y2, given that
6.55 Customers arrive at a department store checkout counter according to a Poisson distribution
with a mean of 7 per hour. In a given two-hour period, what is the probability that 20 or more
customers will arrive at the counter?
6.56 The length of time necessary to tune up a car is exponentially distributed with a mean of
.5 hour. If two cars are waiting for a tune-up and the service times are independent, what is
the probability that the total time for the two tune-ups will exceed 1.5 hours? [Hint: Recall the
result of Example 6.12.]
6.57 Let Y, Y2,..., Y,, be independent random variables such that each Y, has a gamma distribution
with parameters a, and B. That is, the distributions of the Y's might have different a's, but…
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