Derive the Maximum Likelihood Estimator - Mathematics Assignment Help

Assignment Task:

TASK:

Question 1 (20%) 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. x2 . ..• Xn- A Poisson distribution ,vith 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 same type. All of these have been in force for ten years. The numbers of claims made are summarised below, 1\i11111ber ofcla i111s 0 I 2 3 4 5 J\111111ber ofpolicies 18 25 13 10 6 3 Total 75

(a) Use an appropriate statistical test to assess whether a Poisson distribution is an appropriate model for this set of data. (JO)

(b) Obtain an approximate 95o/o confidence interval for the mean of the underlying distribution

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