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Lecturenotes13

# Lecturenotes13 - STAT 430/510 Lecture 13 STAT 430/510...

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STAT 430/510 Lecture 13 STAT 430/510 Probability Hui Nie Lecture 13 June 18th, 2009

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STAT 430/510 Lecture 13 Introduction Many random variables are naturally related to each other. Forecast and actual weather Height and weight Lifetimes of a system and a component These random variables are usually studied together instead of individually The joint behavior of several random variables is described by their joint distribution .
STAT 430/510 Lecture 13 Joint Distribution For two random variables X and Y , the joint cumulative probability distribution function F ( x , y ) is defined for each pair of numbers ( x , y ) by F ( x , y ) = P ( X x and Y y ) The distributions of X and Y can be obtained from the joint cdf F ( x , y ) F X ( x ) = P ( X x ) = P ( X x , Y < ) = F ( x , ) F Y ( y ) = P ( Y y ) = P ( X < , Y y ) = F ( , y ) The distributions F X and F Y are called marginal distributions of X and Y .

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STAT 430/510 Lecture 13 Joint Distribution: Continued All joint probability statements about X and Y can be answered in terms of their joint distribution function.
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Lecturenotes13 - STAT 430/510 Lecture 13 STAT 430/510...

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