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ACTU PS5821 Actuarial Methods - Autumn 2024

Assignment - 1

Assigned 9/6/24, Due 9/14/24

Problem 1. Suppose that the present value of profit on selling one insurance contract is uniformly distributed on [-30, 60], use the normal approximation to calculate the probability of making a profit on selling 10 contracts to 10 unrelated counterparties.

Problem 2. A population has 30% smokers and 70% non-smokers. Future lifetime T is normally distributed with Tsmoker ∼ N(µ = 40, σ2 = 600) and Tnon−smoker ∼ N(µ = 45, σ2 = 500). Calculate the variance of future lifetime for an individual randomly selected from this population.

Problem 3. Suppose a person can memorize a particular passage of text for T years. Let’s model T an exponential distribution with a mean of θ = 1/Y . In a certain population, Y follows the distribution f(y) = 0.25ye−0.5y . What is the probability that a person randomly selected from this population will forget the passage of text after 6 months?