(New page: Category:ECE600 Category:Lecture notes <center><font size= 4> '''Random Variables and Signals''' </font size> <font size= 3> Topic 15: Conditional Distributions for Two Random Va...) |
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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. | 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''' <math>\qquad</math> For random variables X and Y defined on (''S,F | + | '''Definition''' <math>\qquad</math> 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 <br/> |
<center><math>F_{XY}(x,y|M)=\frac{P(\{X\leq x,Y\leq y\}\cap M)}{P(M)},</math></center> | <center><math>F_{XY}(x,y|M)=\frac{P(\{X\leq x,Y\leq y\}\cap M)}{P(M)},</math></center> | ||
A special case of great interest is: | A special case of great interest is: | ||
Revision as of 11:49, 7 November 2013
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
A special case of great interest is:
