home3_2008 - POLITECNICO DI TORINO 01KRR STOCHASTIC...

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POLITECNICO DI TORINO 01KRR STOCHASTIC PROCESSES 2008-2009 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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home3_2008 - POLITECNICO DI TORINO 01KRR STOCHASTIC...

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