Conditional probability

Conditional distribution

When one applies Conditional probability to multiple random variables one obtains a so-called conditional distribution. #m/def/prob For a Discrete random variable we define

𝑝𝑋𝑌(𝑥𝑦)=({𝑋=𝑥}{𝑌=𝑦})=({𝑋=𝑥}{𝑌=𝑦})({𝑌=𝑦})

and for a Continuous random variable

𝑓𝑌𝑋(𝑦𝑥)=𝑓𝑋,𝑌(𝑥,𝑦)𝑓𝑋(𝑥)


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