Definition:Marginal Probability Mass Function

Let $$\left({\Omega, \Sigma, \Pr}\right)$$ be a probability space.

Let $$X: \Pr \to \R$$ and $$Y: \Pr \to \R$$ both be discrete random variables on $$\left({\Omega, \Sigma, \Pr}\right)$$.

Let $$p_{X, Y}$$ be the joint probability mass function of $$X$$ and $$Y$$.

Then the probability mass functions $$p_X$$ and $$p_Y$$ are called the marginal (probability) mass functions of $$X$$ and $$Y$$ respectively.

The marginal mass function can be obtained from the joint mass function:

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