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SPRING 2009
MATH 425
Ralf Spatzier
Homework 4
for Friday, June 5
(1) Suppose
X
is a normal random variable with mean 5. If
P
(
{
X >
9
}
) =
.
2, approxi
mate what is
V ar
(
X
).
(2) In 10,000 independent tosses of a coin, the coin lands heads 5800 times. Is it reason
able to assume that the coin is not fair? Explain.
(3) The number of years that a radio functions is exponentially distributed with param
eter
λ
=
1
8
. If Jones buys a used radio what is the probability that it still functions
after 8 years?
(4) Each item produced by a company is, independently, of acceptable quality with
probability .95. Approximate the probability that at least 10 of the next 150 items
produced are unacceptable.
(5) If
X
is an exponential random variable with parameter
λ
, and
c >
0 show that
cX
is exponential with parameter
λ/c
.
(6) At a bank, the amount of time a teller spends with a customer is an exponential
random variable with mean 5 minutes. If there is a customer in service when you
enter the bank, what is the probability that he/she still will be with the teller after
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This note was uploaded on 04/24/2010 for the course MATH 425 taught by Professor K during the Spring '10 term at University of MichiganDearborn.
 Spring '10
 k
 Math

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