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Simulation: 2018 Tutorial 2 question 4(a)

0 votes
asked Mar 24, 2018 in STA 2004F - Statistical Theory and Inference by Ireneus (540 points)
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.

2 Answers

+2 votes
answered Mar 25, 2018 by Pandy (2,850 points)

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.

0 votes
answered Apr 2, 2018 by PaulBotes (760 points)

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.