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- 5 Suppose the distribution function of the continuous random variable is (1-e *, -5x x>0; F(x) = 0, x3); (2) the density function f(x)Suppose insurance loss X follows a Pareto distribution with mean 200 and variance 60,000. (a) Find α, and θ. (b) Find eX(100). (c) Find VaR0.95(X). (c) Find TVaR0.95(X)Let X₁,..., Xn be an iid random sample from a Uniform(0, 0), where 0 > 0. Let X(n) = max{X₁, (a) Find the mean and variance of X(n). (b) Find the limiting distribution of Zn = n (0 – X (n)). (c) Find the limiting distribution of log(Zn). Xn}
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