random sample of n insurance policies of a particular type. all of which have been in force for 10 years. has been taken.

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A random sample of n insurance policies of a particular type. all of which have been in force for 10 years. has been taken. The numbers of claims made are x1. s2 .,..s. A

Poisson distribution with parameter A is to be used to model the number of claims.

(i) Derive the maximum likelihood estimator of A.(5)

(ii) An insurance company has taken a random sample of 75 policies of the sametpe. All of these have been in force for ten years. The numbers of claims

made are summarised below.

Number of cluins Number of policies

O 1$

1 25

2 13

3 lO

4 6

5 3

Total 75

(a) Use an appropriate statistical test to assess whether a Poisson

distribution is an appropriate model for this set of data.

(10)

(b) Obtam an approximate 9500 confidence interval for the mean of the underlying distrihuùon.(5)

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