Simulation: 2018 Tutorial 2 question 4(a)

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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.

answered Mar 25 by (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.

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.