Question: 15. For n 1, let Xn be a continuous random variable with the probability density function X n s are called Pareto random variables

15. For n ≥ 1, let Xn be a continuous random variable with the probability density function

Cn if x Cn xn+1 fn(2) otherwise.

Xn’s are called Pareto random variables and are used to study income distributions.

(a) Calculate cn, n ≥ 1.

(b) Find E(Xn), n ≥ 1.

(c) Determine the probability density function of Zn = lnXn, n ≥ 1.

(d) For what values of m does E(Xm+1 n ) exist?

Cn if x Cn xn+1 fn(2) otherwise.

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