From Computational Statistics (CSE383M and CS395T)
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A joint probability distribution is a probability distribution that depends on multiple variables (e.g. P(x,y,z)). In many situations, you may only care about the probability distribution of one variable (e.g. P(x)), and do not care about the probability of the other variables. Marginalization allows us to eliminate the dependence of the probability distribution on a given variable by "integrating it out".

For instance:

Let <math>P(x,y,z)</math> be the probability we are interested in terms of <math>x,y,\mbox{ and }z</math> Then in order to find <math>P(x,y)</math>, we compute it in the following manner: <math>P(x,y) = \int P(x,y,z) dz</math>