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 February 9th, 2014, 06:43 AM #1 Newbie   Joined: Feb 2014 Posts: 1 Thanks: 0 Homework help - Generating random variable Hi, I have a problem on the following homework assignment: Suppose that X and Y are discrete random variables with a joint probability mass function p_XY (x, y). Procedure is the following: a. Generate X ? p_X (x). b. Accept X with probability p(y|X). c. If X is accepted, terminate and return X. Otherwise go to Step a. Show that this procedure generates a random variable X ? p_X|Y (x|y). I would've been grateful for any help. Tnx
 February 9th, 2014, 11:11 AM #2 Newbie   Joined: Feb 2014 Posts: 3 Thanks: 0 Re: Homework help - Generating random variable I am assuming that by "generate some random variable" you mean to generate random outcomes that follow that particular distribution. The idea is to generate first random outcomes from a Uniform Random Variable in (0,1) for which there are plenty libraries. For instance, in java you would do something like: double uniformOutcome; Random rand; uniformOutcome = rand.nextDouble(); The generated number is a "pseudorandom" meaning it is not really random but rather a sequence of numbers that simulate randomness based on a "seed" number. Typically this formulas use modulos. Once you've your uniform random draw you just need to use $F_{X}^{-1}(uniformOutcome)$. In step b), generate similarly a random draw from the distribution $F_{y|X}^{-1}(uniformOutcome2)$and accept if outcome is bigger than a third uniform Outcome Step c), just do as told. To prove this, looks like a consequence of bayes theorem, i.e., p(x|y) = p(x) * p(y|x) / p(y), the details I leave them to you.

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