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Math Help - Let random variate X take on a value 1 an 0...show that X and Y are independent

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    Let random variate X take on a value 1 an 0...show that X and Y are independent

    Question :
    Let random variate X take on a values 1 and 0 with the probabilities p_1 and q_1 = 1 - p_1 respectively and let Y take the values 1 and 0 with probabilities p_2 and q_2 respectively . If the correlation coefficient between X and Y is 0, show that X and Y are independent.
    Last edited by zorro; December 13th 2009 at 03:49 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    If the correlation, hence the covariance is zero we have

    E(XY)=E(X)E(Y)=p_1p_2

    since E(X)=p_1 and E(Y)=p_2

    That means P(X=1,Y=1)=p_1p_2=P(X=1)P(Y=1)

    Now you need to fill in the other 3 spots of the 2 by 2 joint probability distribution.

    That is... P(X=1,Y=0)=P(X=1)P(Y=0)

    P(X=0,Y=1)=P(X=0)P(Y=1) and P(X=0,Y=0)=P(X=0)P(Y=0).


    and this part doesn't make sense....'show that X and Y is 0'
    Last edited by matheagle; December 4th 2009 at 10:00 PM.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    If the correlation, hence the covariance is zero we have

    E(XY)=E(X)E(Y)=p_1p_2

    since E(X)=p_1 and E(Y)=p_2

    That means P(X=1,Y=1)=p_1p_2=P(X=1)P(Y=1)

    Now you need to fill in the other 3 spots of the 2 by 2 joint probability distribution.

    That is... P(X=1,Y=0)=P(X=1)P(Y=0)

    P(X=0,Y=1)=P(X=0)P(Y=1) and P(X=0,Y=0)=P(X=0)P(Y=0).


    and this part doesn't make sense....'show that X and Y is 0'

    It is 'show that x and y are independent '


    I couldnt get u mite ............where are u getting at.....
    Last edited by mr fantastic; December 25th 2009 at 07:16 PM. Reason: Merged posts
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