2. (5 points) Suppose that loss severity, X, has a twoparameter Pareto distribution with parameters a and 6. Assume that there is an ordinary deductible of d per loss. (a) Determine the cdf of the claim payment per payment random variable. Identify the name of the distribution, and the values of its parameters. (b) A loss severity distribution is a two-parameter Pareto distribution with shape parameter 3 and scale parameter 250. An insurance company will pay the amount of each loss in excess of a deductible of 100. Calculate the variance of the amount paid by the insurance company for one loss, including the possibility that the amount paid is 0. Make use of the law of total expectation for any moment calculations. Recall: if Y = g(X), the law of total expectation states that for some threshold value d: E[Y] = E[g(X)|X g d]Pr(X g d) + E[g(X)|X > d]Pr(X > d)