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## Joint Distribution

When a pair of random variables is considered, a joint density function is used to compute probabilities constructed from the random variables and simultaneously. Given the joint density function , the distribution for each of and is called the marginal distribution. The marginal density functions of and , denoted by and , are given respectively by

and

Conditional probability distributions. Suppose that two random variables and has a joint density function . If , then we can define the conditional density function given by

Similarly we can define the conditional density function given by

if . Then, clearly we have the following relation