Problem 2 Generating Continuous Random Variables: One can generate samples of any random variable for a given proba- bil

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Problem 2 Generating Continuous Random Variables One Can Generate Samples Of Any Random Variable For A Given Proba Bil 1 (38.53 KiB) Viewed 39 times

Problem 2 Generating Continuous Random Variables: One can generate samples of any random variable for a given proba- bility density function fx(x) (where X is a random variable) by using a uniform distribution defined over (0,1). The procedure for doing this consists of the following three steps: 1. Determine the function u = f fx (t) dt 2. Determine its inverse x = g(u) 3. If U is a sample uniformly distributed on (0,1), then X = 9(U) is a sample whose distribution is given by fx(x). The random variable X has an Rayleigh distribution if its probability density function is given by fx (*) (a) Determine a function X =9(U) such that X has a Rayleigh distribution using the procedure described above. (b) Write a Matlab program that simulates this distribution and compares it to the theoretical Rayleigh distribution. You can use the rand, hist, and bar functions. -rº/20%, 1 € (0,20). al