5. A collection of insurance policies consists of two types. 25% of policies are Type 1 and 75% of policies are Type 2. For a policy of Type 1, the loss amount per year follows an exponential distribution with mean 200, and for a policy of Type 2, the loss amount per year follows a Pareto distribution with parameters ? = 3 and ? = 200. For a policy chosen at random from the entire collection of both types of policies, find the probability that the annual loss will be less than 100, and find the average loss.
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Given that 25% of policies are Type 1 and 75% are Type 2: For Type 1 (exponential distribution with mean 200): Probability of annual loss less than 100 = ∫[0,100] 1/200 * e^(-x/200) dx Using the exponential distribution formula, this integral evaluates to 0.3944. Show more…
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