10. Recall the claims model of exercise 18 of chapter 7:

(a) For both the individual and aggregate risk model estimates of the mean and variance of claims, apply the Chebyshev inequality in (8.36) to estimate the probability that claims exceed $8 million, $9.5 million, and $11 million.

(b) Estimate the probabilities from part

(a) directly by a simulation method, with 1000 simulations, using (8.38).

(c) Using the simulations from part (b), and C0 ¼ $7.5 million, estimate the conditional means and variances of the two models, and with these results estimate the probabilities in part

(a) using (8.40).