Question 3 [15 marks] Let X be a random variable with the Pareto probability density function (pdf) given by fx(x) = r 2 8. 0. where a and / are positive constants. a. Find Fx(x), the cumulative distribution function (cdf) of X. b. Find a transformation G(Y) such that, if Y has a uniform distribution on the interval (0. 1). G(Y ) has the same distribution as the random variable X. c. Define Z = 1/X. From first principles derive the cdf and the pdf of Z. d. The random variables X1, X2, ...; X, are independent and identically distributed with the pdf fx(x). Let X() = min{X1, X2. .... Xn). Show that the cdf Fx(x) of Xon is (1-(9) Fx((I) = e. Show that, for = > 0, P(IX(1) - B|