NotesSep8 - Computation of the marginal pmfs Let (X, Y ) be...

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Computation of the marginal pmfs Let ( X,Y ) be a discrete random vector with a joint pmf p X,Y ( a i ,b j ). The probability mass functions of X and Y are called marginal pmfs, p X ( a i ) and p Y ( b j ). By the formula of total probability p X ( a i ) = P ( X = a i ) = X j P ( X = a i ,Y = b j ) = X j p X,Y ( a i ,b j ) . Similarly, p Y ( b j ) = X i p X,Y ( a i ,b j ) .
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In the previous example one obtains the marginal pmf of X by summing up the table row-wise, and the marginal pmf of Y by summing up the table column-wise a i /b j 0 1 2 3 p X ( a i ) 0 .840 .030 .020 .010 .900 1 .060 .010 .008 .002 .080 2 .010 .005 .004 .001 .020 p Y ( b j ) .910 .045 .032 .013 1
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Continuous random vectors A random vector ( X,Y ) is continuous if it has a (joint) density . Joint probability density function ( joint pdf ) of a continuous random vector ( X,Y ) is a non- negative function f X,Y ( x,y ) such that for any two-dimensional set C P (( X,Y ) C ) = ZZ C f X,Y ( x,y ) dxdy. In particular, if
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NotesSep8 - Computation of the marginal pmfs Let (X, Y ) be...

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