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SEP 2016- Ques 4 -UK Papers

A

Anjum

Member
Consider two portfolios, A and B, of insurance policies and denote by XA the number of claims received in portfolio A and by XB the number of claims received in portfolio B during a calendar year. The observed numbers of claims received during the last calendar year are 134 for portfolio A and 91 for portfolio B. XA and XB are assumed to be independent and to have Poisson distributions with unknown parameters A and B. Determine an approximate 99% confidence interval for the difference A  B. You may use an appropriate normal distribution.

Kindly explain the below points-
1.why is sample size=1
2.why have we taken Beta(a)=134
 
Since the no. the claims observed are from last year i.e. only one year, So sample size is one. And 134 and 91 are the observed no. of claims from Portfolio A and B respectively.
Hence, the 99% CI for difference in beta A and beta B should be:
(X1-X2)±prob.[(X1/n1)+(X2/n2)]^1/2
(134-91)±2.5758[(134/1)+(91/1)]^1/2
 
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