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)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 PISTONE
 Probability, Probability theory, Politecnico di Torino, S. Ross, Probability modelsEight edition, newly insured policyholder

Click to edit the document details