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For n 1 let x be a continuous random variable with the


For n > 1, let X„ be a continuous random variable with the probability density function

711_random variable with the probability density function.png

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

(a) Calculate cn, 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,7+1) exist?

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Basic Statistics: For n 1 let x be a continuous random variable with the
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