Conditional probability

Conditional distribution

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

𝑝𝑋∣𝑌(𝑥∣𝑦)=ℙ({𝑋=𝑥}∣{𝑌=𝑦})=ℙ({𝑋=𝑥}∩{𝑌=𝑦})ℙ({𝑌=𝑦})

and for a Continuous random variable

𝑓𝑌∣𝑋(𝑦∣𝑥)=𝑓𝑋,𝑌(𝑥,𝑦)𝑓𝑋(𝑥)

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