Exam FAM sample questions, with full solutions

Losses follow a Pareto distribution with $\alpha = 3$ and $\theta = 2{,}000$. An insurance policy has an ordinary deductible of 500.

Calculate the expected payment per loss.

The number of claims $N$ is a member of the (a, b, 0) class with $a$ $= -0.25$ and $b$ $= 1.25$.

Calculate $P(N$ $= 2)$.

Losses on a dental plan follow an exponential distribution with mean $\theta$. A random sample of 8 losses is: 120, 340, 85, 610, 230, 455, 190, 970.

Using the maximum likelihood estimate of $\theta$, calculate the estimated probability that a loss exceeds 500.

The number of claims per exposure unit follows a Poisson distribution with mean 0.04. Full credibility for claim frequency requires that the observed value is within 5% of its expected value with probability 0.95. Use $y_p$ $= 1.960$ from the standard normal table.

Calculate the number of exposure units needed for full credibility.

An actuary has selected the following age-to-age factors for reported losses:

At December 31, 2025, reported losses for accident year 2024 are $1,840,000.

Using the chain-ladder method, calculate the estimated ultimate losses for accident year 2024.