Question: 13 For n 1, let X,, be a continuous random variable with the probability density function f(x) = = {C/x+ C/x+ if x C otherwise.

13 For n 1, let X,, be a continuous random variable with the probability density function f(x) = = {C/x+ C/x+ if x C otherwise. X's are called Pareto random variables and are used to study income distributions.

(a) Calculate

c. n 1.

(b) Find E(X,), n 1.

(c) Determine the density function of Z = In X,, n 1.

(d) For what values of m does E(X+) exist?

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