
#41




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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