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The distributions of aggregate claims from two risks, denoted by S, andS,, are as follows: S, has a compound Poisson distribution with parameter 100 and distribution function F (x) =1-exp(-r/0 and S, has a compound Poisson distribution with parameter 200 and distribution function F, (x) =1-exp(-x/ #), x>0. If S, and $2 are independent, what is the distribution of $1 + $2?The aggregate claims from a risk have a compound Poisson distribution with parameter 4. Individual claim amounts (in pounds) have a Pareto distribution with parameters a-3 and 2 -1,000. The insurer of this risk calculates the premium using a premium loading factor of 0.2 (ie it charges 20% in excess of the risk premium). The insurer is considering effecting excess of loss reinsurance with retention limit El.0(0. The reinsurance premium would be calculated using a premium loading factor of 0.3. The insurer's profit is defined to be the premium charged by the insurer less the reinsurance premium and less the claims paid by the insurer, net of reinsurance. (i) Show that the insurer's expected profit before reinsurance is 1001/. (ii) Calculate the insurer's expected profit after effecting the reinsurance. and hence find the percentage reduction in the insurer's expected profit. (iii) Calculate the percentage reduction in the standard deviation of the insurer's profit as a result of effecting the reinsurance