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#41
03-20-2017, 09:45 PM
 mathematicalhype Member CAS SOA Join Date: Nov 2013 Posts: 270

Soa Sample Question 11:
Losses on a company’s insurance policies follow a Pareto distribution with
probability density function: f(x/theta) = theta / (x+theta)^2.
For half of the company’s policies, theta = 1, while for the other half, theta = 3.
For a randomly selected policy, losses in Year 1 were 5.
Calculate the posterior probability that losses for this policy in Year 2 will exceed 8.

Could we have solved this using the formula for posterior density,
= (prior * likelihood) / (integral of (prior * likelihood) ) ?
The solution solves by finding
P(x2 > 8 | x1=5) using P(theta = 1 | x = 5) and P(theta = 3 | x = 5).
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#42
06-22-2017, 01:07 PM
 StayCoolKD Member CAS Join Date: Sep 2014 College: Alumni University of Washington Posts: 272