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POLITECNICO DI TORINO
01KRR STOCHASTIC PROCESSES 20082009
HOMEWORK 4: DUE TO OCT 6, 2008
Ref
. S. Ross,
Introduction to Probability models
Eight edition, Chapter 3.
Exercises
Ross 22
Suppose that independent trials, each of which is equally likely to
have any of
m
possible outcomes, are performed until the same outcome occurs
k
consecutive times. If
N
denotes the number of trials, show that
E
[
N
] =
m
k

1
m

1
.
Ross 3.28
An automobile insurance company classiﬁes each of its policyholders
as being of one of the types
i
= 1
,...,k
. It supposes that the numbers of
accidents that a type
i
policyholder has in successive years are independent
Poisson random variables with mean
λ
i
,
i
= 1
,...,k
. The probability that a
newly insured policyholder is type
i
is
p
i
,
∑
k
i
=1
p
i
= 1.
(i)
Given that a policyholder had
n
accidents in her ﬁrst year, what is the
expected number that she has in her second year?
(ii)
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 Spring '08
 PISTONE
 Probability

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