2022-02-14

What general form of the mass function of a conditional probability distribution for discrete random variables?

patriette65s

Step 1
Let X and Y be two discrete random variables. The conditional probability mass function of X given $Y=y$ is a function
${p}_{X\mid Y=y}:\mathbb{R}\to \left[0,1\right]$ such that
${p}_{X\mid Y=y}\left(x\right)=P\left(X=x\mid Y=y\right)$
for any $x\in \mathbb{R}$
where $P\left(X=x\mid Y=y\right)$ is the probability that $X=x$
given that $Y=y$

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