The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This distribution is often used in statistical modeling. (a) Find the CDF of a Pareto r.v. with...

The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This distribution is often used in statistical modeling. (a) Find the CDF of a Pareto r.v. with parameter a; check that it is a valid CDF. (b) Suppose that for a simulation you want to run, you need to generate i.i.d. Pareto(a) r.v.s. You have a computer that knows how to generate i.i.d. Unif(0, 1) r.v.s but does not know how to generate Pareto r.v.s. Show how to do this.