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The joint probability function for two variables is a probability function whose domain is a subset of two dimensional space. The joint probability function for discrete random variables X and Y is given as

pr(x, y) = pr(X = x and Y = y). If X and Y are independent random variables then this will equal pr(X =x)*pr(Y = y).

For continuous variables, the joint funtion is defined analogously:

f(x, y) = pr(X < x and Y < y).

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Q: What is joint probability function?
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