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Math Help - How to calculate covariance given a probability distribution table.

  1. #1
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    Angry How to calculate covariance given a probability distribution table.

    Hello all,

    The probability distribution table is:-
    Code:
                    Y
              1     2     3
    
         1   .1   .05  .02
    
    X   2   .1   .35  .05
    
         3   .03  .1   .2
    Mean of x = 2.16 ; Mean of y = 2.04
    Calculation of covariance is; ( ( 1 - 2.16 ) * ( 1 - 2.04 ) + ( 2 - 2.16 ) * ( 2 - 2.04 ) + ( 3 - 2.16 ) * ( 3 - 2.04 ) ) / 3 = 0.67

    Even if we multiply probabilities; ( ( 1 - 2.16 ) * ( 1 - 2.04 ) * (.1) + ( 2 - 2.16 ) * ( 2 - 2.04 ) * (.35) + ( 3 - 2.16 ) * ( 3 - 2.04 ) * (.2) ) / 3 = 0.094

    However COV(X,Y) in the answers is 0.23. Can someone show me how to correctly calculate covariance using the usual covariance formula.

    Thanks
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  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
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    Thanks
    5
    1 you have to do all nine positions.
    2 you should use the short cut formula E(XY)-E(X)E(Y)
    3 and you do need to multiply by the probabilities

    E(XY)=(1)(1)(.1)+..... for all nine possibilities.
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