1. Conditional distribution

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Definition (Conditional distribution).

, discrete RV the conditional pmf of given
only when

Remark.

Definition (Conditional Cumulative Distribution function ).

, discrete RV the conditional (cumulative ) distribution function (conditional CDF)
of given

If , are independent

Example

Important

Refer 6.4 Conditional Distribution: Discrete Case from A first course in Probability by - Sheldon Ross (page number: 248) Conditional Distributions
Example 4a 4b 4c 4d (Basically all the examples ) which were done in class but not completely written in this notes. Don't worry they are about the same

  1. If pmf of and

find

  1. is Poisson() is Poisson()
    conditional distribution of given X+

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3. possible outcome with probability independent trials

suppose given

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