5)[20 points] Consider an insured, an insurer, and a reinsurer. Consider a loss X with E[X] = 1000 and VAR[X] = 5000. The insurer collects a premium 1.01E [X] The insurer will pay X I (X ) and the insurer will pay I(X), where 0 5 [(X) g X. The reinsurer asks E[I(X)] + 0.05VAR[I(X)] as a premium. The insurer wants to nd I (X) that maximizes his expected prot such that the variance of the retained risk satises VAR[X I(X)] = 2000.00. Find the optimal f(X)