MA540
Page  1
Homework 3
1)
Problem 8 Page 228
Suppose that 10 trains arrive independently at a station every day, each at random time between
10:00am and 11:00am. What is the expected number and the variance of those that arrive
between 10:15am and 10:28am?
Solution:
Call a train that arrives between 10:15am and 10:28am a success. Then
p
, the probability of
success is
Therefore, the expected value and the variance of the number of trains that arrive in the given
period are
2)
Problem 9 Page 228
Suppose that a certain bank returns bad checks at a Poisson rate of three per day. What is the
probability that this bank returns at most four bad checks during the next two days?
Solution:
The number of checks returned during next two days is Poisson with
. The desired
probability is
3)
Problem 14 Page 229
Past experience shows that 30% of the customers entering Harry’s Clothing Store will make a
purchase. Of the customers who make a purchase, 85% use credit cards. Let
X
be the number of
the next six customers who enter the store, make a purchase, and use a credit card. Find the
probability mass function, the expected value, and the variance of
X
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 Spring '10
 prasad
 Variance, Probability theory, Credit card, $15, $30

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