13. For n 1, let Xn be a continuous random variable with the probability density function...
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13. For n ≥ 1, let Xn be a continuous random variable with the probability density function fn(x) = cn xn+1 if x ≥ cn 0 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 density function of Zn = ln Xn, n ≥ 1.
(d) For what values of m does E(Xm+1 n ) exist?
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Related Book For 
Fundamentals Of Probability With Stochastic Processes
ISBN: 9780131453401
3rd Edition
Authors: Saeed Ghahramani
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