Let pn, n = 0, 1, 2, ... , be the probability that an automobile policyholder will file

Chapter 1, Problem 1.1-16

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QUESTION:

Let pn, n = 0, 1, 2, ... , be the probability that an automobile policyholder will file for n claims in a five-year period. The actuary involved makes the assumption that pn+1 = (1/4)pn. What is the probability that the holder will file two or more claims during this period?

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QUESTION:

Let pn, n = 0, 1, 2, ... , be the probability that an automobile policyholder will file for n claims in a five-year period. The actuary involved makes the assumption that pn+1 = (1/4)pn. What is the probability that the holder will file two or more claims during this period?

ANSWER:

Step 1 of 4

The values of  and  are obtained below:

From the information given, the actuary involved makes the assumption that

For ,

For ,

Similarly,

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