10 Example Class 8

# 10 Example Class 8 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 8 Review Conditional Distributions and Conditional Expectation For any two events E and F, the conditional probability of E given F is defined by P ( E | F ) = P ( E ∩ F ) P ( F ) provided that P(F) > Let ( X,Y ) be a discrete bivariate random vector with joint pmf p ( x,y ) and marginal pmfs p x ( x ) and p y ( y ). The conditional pmf of Y given that X = x is the function of y denoted by p Y | X ( y | x ), where p X ( x ) > p Y | X ( y | x ) = P ( Y = y | X = x ) = P ( Y = y,X = x ) P ( X = x ) = p ( x,y ) p X ( x ) If X is independent of Y, then the conditional pmf becomes p Y | X ( y | x ) = p ( x,y ) p X ( x ) = p X ( x ) p Y ( y ) p X ( x ) = p Y ( y ) For continuous random variables, the conditional distributions are defined as: f Y | X ( y | x ) = f ( x,y ) f X ( x ) provided that f X ( x ) > f X | Y ( x | y ) = f ( x,y ) f Y ( y ) provided that f Y (...
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## This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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10 Example Class 8 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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