Question: An insurance company believes that claim amounts in a certain portfolio of policies follow a normal distribution. An analyst chose 61 policies at random which gave a sample mean of £523 and a sample standard deviation of £81. The company assumes that the true mean and standard deviation of claim amounts are the same as those in the sample. The number of claims per month for the portfolio follows a Poisson process with mean 250. (iv) Determine the mean and standard deviation for the total annual amount of claims in the portfolio. Answer in the examiner's report: (iv) Now the rate of claims is 12 × = 3000 [1] Mean = _new * mu_claims = 3000 ∗ 523 = 1,569,000 [1] Standard deviation = sqrt(lamda_annual) * sqrt(sigma_claim^2+mu^2) = √3000 ∗ √(812 + 5232) =28987 [2] can anyone explain how the standard deviation is calculated?
It's calculated using the formula for var(S) given on p16 of the Tables. However, this is not covered in CS1. It is part of the CS2 syllabus.
