Using a standard uniform random variable,[0,1], we want to generate samples of a random variable, X, whose probability density function (pdf), p, (x), is sketched below. Px(x) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 02 0.1 0 -3 -2.5 -2 -1.5 x -1 -0.5 0 andom a) Write down the mathematical expression of the above pdf. Check whether it is a valid pdf. b) Find the required transformation equation. c) Using MATLAB or a similar computer program, generate 100 samples of X and sketch their histogram. d) On the histogram, sketch the true pdf. e) Repeat parts c) and d) for 1000 and 10000 samples of X. f) Comment on your results. g) In your report, include your software codes with explanations of steps.

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