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List the three main perils typically covered by employer's liability insurance. 131 An insurer wishes to estimate the expected number of claims, 2. on a particular type of policy. Prior beliefs about 2 are represented by a Gamma distribution with density function f(X) = - an-left (). > 0 ). r(a) For an estimate, d, of ) the loss function is defined as Show that the expected loss is given by E(LO., d)) = a(0+1) 2da. -+ 2c2 B and hence determine the optimal estimate for A under the Bayes rule. [5] (1) Explain the disadvantages of using truly random, as opposed to pseudo- random, numbers. [3] (Hi) List four methods for the generation of random variates. [21 [Total 5] Yet = 1. 2, 3. ... is a time series defined by Y - D.BY,_ = Z, + 0.2Z,- where Z, / - 0, 1, ... is a sequence of independent zero-mean variables with common variance q Derive the autocorrelation pp * = 0, 1, 2, ... [6]