Simulation: 2018 Tutorial 2 question 4(a)

Question

What does the following question trying to say? 

Given a random variable X with the following density

                                        f(x)=5/x^6 for x greater than or equal to 1

a) Explain how you would simulate realisations from from X when supplied with uniform random numbers.

Answer 1

My understanding is that they're asking you to simulate the random variable with the given PDF \(f(x)\), but making use of the Uniform distribution instead.

This is generally done when one can't simulate realizations of a random variable directly.

I imagine they're wanting you to use the Probability Integral Transform.

Answer 2

Find the CDF, \(F_x(x)\) of the distribution and then find its inverse \(F^{-1}_x(x)\).  \(F^{-1}_x(U)\) where \(U \sim U(0,1)\) will then admit realisations from the random variable.