provide accurate answers for this question. you The number of claims in a week that arises from a certain group of insurance policies has a Poi() distribution. In the last

provide accurate answers for this question. you The number of claims in a week that arises from a certain group of insurance policies
has a Poi() distribution. In the last 2 weeks, the numbers of claims incurred were 7
and 11, respectively.
(i)
Derive the posterior distribution given that the prior distribution for & is:
(@)
gauuna with parameters o =7 and 1 =0.5
(b)
uniform on the integers 8. 10 and 12.
[5]
(ii)
Hence for each case in part (i) obtain the Bayesian estimate of / using a:
(a) quadratic loss function
(b)
absolute loss function
(c)
zem-one loss function.
[8]
[Total 13] Consider aggregate claims over a period of 1 year. S. on a portfolio of general
insurance policies:
S = X1+X2+…+ XN
The number of claims each year, / , has a Poisson distribution with mean 12.
X. Xy… are assumed to be random variables, independent of each other and
independent of N , with the following distribution:
() =0.01e-QOlx
0 <x <f200
P(X – (200) – e-
The insurer effects excess of loss reinsurance with a retention of f100. Annual
aggregate claims paid by the reinsurer are denoted by SR.
Calculate E(SR), van(SR) and E (SR – E(SR))]].
[12]

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