ECE600 F13 Conditional Distributions for Two Random Variables mhossain - Rhea

Random Variables and Signals

Topic 15: Conditional Distributions for Two Random Variables

Conditional Distributions

There are many applications of probability theory where we want to know the probabilistic behavior of a random variable Y given the value of another random variable X. We get this using conditional distributions.

'Definition $\qquad$ For random variables X and Y defined on (S,F,P), the joint cdf of X and Y given an event M ∈ F, with P(M) >0, is

F_{XY}(x,y|M)=\frac{P(\{X\leq x,Y\leq y\}\cap M)}{P(M)},

A special case of great interest is:

ECE600 F13 Conditional Distributions for Two Random Variables mhossain - Rhea

Conditional Distributions

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