A random variable X has the Pareto distribution P (c, ) if its density is c c/xc+1, 0 < < x, 0 <

A random variable X has the Pareto distribution P

(c, τ ) if its density is cτ c/xc+1, 0 < τ < x, 0 < C.

(i) Show that this defines a probability density.

(ii) If X has distribution P

(c, τ ), then Y = log X has exponential distribution E(ξ,

b) with ξ = log τ , b = 1/c.

(iii) If X1,..., Xn is a sample from P

(c, τ ), use (ii) and