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crib_sheet2 - Crib sheet for Exam II Chapter 5: Joint...

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Unformatted text preview: Crib sheet for Exam II Chapter 5: Joint Probability Distributions The marginal probability mass functions of two discrete rvs X and Y , denoted by p X ( x ) = P ( X = x ) and p Y ( y ) = P ( Y = y ), respectively are given by: p X ( x ) = X y p ( x,y ) p Y ( y ) = X x p ( x,y ) The marginal probability density function of two continuous rvs X and Y , denoted by f X ( x ) and f Y ( y ), respectively are given by: f X ( x ) = Z - f ( x,y ) dy f Y ( y ) = Z - f ( x,y ) dx Two r.v. X,Y are independent if for every pair of ( x,y ): Discrete: p ( x,y ) = p X ( x ) p Y ( y ) Continuous: f ( x,y ) = f X ( x ) f Y ( y ) Conditional pdf/pmf: f Y | X ( y | x ) = f ( x,y ) f X ( x ) ,- < y < p Y | X ( y | x ) = p ( x,y ) p X ( x ) ,- < y < Covariance and Correlation coefficient of two rvs X,Y E [ h ( X,Y )] = X x X y h ( x,y ) p ( x,y ) E [ h ( X,Y )] = Z - Z - h ( x,y ) f ( x,y ) dxdy Cov ( X,Y ) = E [( X- x )( Y- y )] =...
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This note was uploaded on 03/29/2008 for the course STAT 211 taught by Professor Parzen during the Spring '07 term at Texas A&M.

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crib_sheet2 - Crib sheet for Exam II Chapter 5: Joint...

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