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# Lecturenotes17 - STAT 430/510 Lecture 17 STAT 430/510...

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STAT 430/510 Lecture 17 STAT 430/510 Probability Hui Nie Lecture 17 June 25th, 2009

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STAT 430/510 Lecture 17 Review Discuss the joint probability distribution in Chapter 6 Introduce properties of expectations in Chapter 7
STAT 430/510 Lecture 17 Recall: Deﬁnition of Expected Value The expected value of the discrete random variable X with probability mass function p ( x ) is given by E [ X ] = X x xp ( x ) The expected value of the continuous random variable X with probability density function f ( x ) is given by E [ X ] = Z -∞ xf ( x ) dx If P ( a X b ) = 1, then a E [ X ] b

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STAT 430/510 Lecture 17 Expectation of a Function of Two Random Variables If X and Y have a joint probability mass function p ( x , y ) , then E [ g ( X , Y )] = X y X x g ( x , y ) p ( x , y ) If X and Y have a joint probability density function f ( x , y ) , then E [ g ( X , Y )] = Z -∞ Z -∞ g ( x , y ) f ( x , y ) dxdy
STAT 430/510 Lecture 17 Example An accident occurs at a point X that is uniformly distributed on a road of length L . At the time of the accident, an ambulance is at a location Y that is also uniformly distributed on the road. Assuming that X and Y are independent, ﬁnd the expected distance between the ambulance and the point of the accident.

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## This note was uploaded on 06/28/2009 for the course STAT 430 taught by Professor Krieger during the Summer '08 term at UPenn.

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Lecturenotes17 - STAT 430/510 Lecture 17 STAT 430/510...

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