marginal distribution

probability

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June 30, 2026

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A marginal distribution is a probability distribution of a subset of random variables from a larger set of random variables. It is derived from the joint probability distribution of these variables. For instance, if you have the joint distribution of two random variables, X and Y, the marginal distribution of X is found by summing the probabilities of X across all possible values of Y. This process effectively "removes" the influence of Y to focus solely on the probabilities associated with X.1

Marginal distributions are useful for understanding the behavior of individual variables within a system, even when they are related to other variables. For example, when rolling two dice, the marginal distribution of the sum of the numbers can be calculated separately from the distribution of the number of even numbers appearing.1

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probability theory
Probability distribution
Often f is called the marginal distribution of X to emphasize its relation to the joint distribution of X and Y. Similarly, g(y_j) = Σ_ih(x_i, y_j) is the (marginal) distribution of Y. The random variables X and Y are defined to be
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Often f is called the marginal distribution of X to emphasize its relation to the joint distribution of X and Y. Similarly, g(y_j) = Σ_ih(x_i, y_j) is the (marginal) distribution of Y. The random variables X and Y are defined to be
Read More