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Math Help - Covariance

  1. #1
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    Covariance

    The discrete variables A and B can each take any of the integer values {0,1,2,3}, and their joint
    probability function is tabulated below.

    B 0 1 2 3
    A 0 |0.00 0.10 0.12 0.03
    1 |0.15 0.20 0.08 0.02
    2 |0.14 0.09 0.04 0.00
    3 |0.02 0.01 0.00 0.00

    a)Find the covariance of A and B.
    b)Are A and B independent ? If not, then why not ?

    i know for covariance the forumula is cov= E[AB]-E[A]E[B]
    I have E[A]=1.08 ,E[B]=1.03, Var[A]=0.6336, Var[B]=0.7491

    so yeah i kinda need help with the E[AB] part
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  2. #2
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    Re: Covariance

    Hello,

    You'll have to compute the probabilities for the values of AB.

    AB can only equal 0,1,2,3,4,6.

    0 : A or B is 0, that is .15+.14+.02 + .10+.12+.03
    1 : A=1, B=1 that is .20
    2 : A=1, B=2 or A=2,B=1 that is .09+.08

    etc...
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  3. #3
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    Re: Covariance

    You can use formula
    \mathbb E(AB) =\sum_{\text{all cases } a,b} a b \mathbb P (A=a, B=b)
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