The marginal distribution refers to the probability distribution of a subset of variables contained in a joint distribution.

The marginal distribution refers to the probability distribution of a subset of variables contained in a joint distribution. It is obtained by "summing over" all outcomes of the other variables in the joint distribution in case of discrete variables, and "integrating over" all outcomes of the other variable in case of continuous variables.

Thus, if $P(x_1,x_2,\ldots,x_n)$ represents a discrete joint distribution, the marginal distribution of $x_i$ is:

$$P(x_i) = \sum_{x_1,x_2,\ldots,x_{i-1},x_{i+1},\ldots x_n} P(x_1,x_2,\ldots,x_n)$$

The summation is over all possible outcomes of the indicated variables. Similarly, for the case of a continuous joint distribution:

$$P(x_i) = \int \int \ldots \int P(x_1,x_2,\ldots,x_n) dx_1 dx_2 \ldots dx_{i-1} dx_{x+1} \ldots dx_{n}$$

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