Law of Total Variance (SOA Exam P – Probability – Multivariate Random Variables)

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After completing this video you should be able to:

- Calculate variance and standard deviation for conditional and marginal probability distributions for discrete random variables only.

Example:

An insurance policy will reimburse only one claim per year. For a random policyholder, there is a 20% probability of no loss in the next year, in which case the claim amount is 0. If a loss occurs in the next year, the claim amount is normally distributed with mean 1000 and standard deviation 400.

Calculate the variance of the claim amount in the next year for a random policyholder.