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Math Help - Joint Probability Distribution

  1. #1
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    Joint Probability Distribution

    Don't know what to do and need your help!

    If Y1 and Y2 are random variables of the discrete type having the probability distribution

    f(y1,y2) = (y1 + 2y2)/18, (y1,y2) = {(1,1),(1,2),(2,1),(2,2)}

    (a) Find E(Y1 + 2Y2) and V(Y1 + 2Y2).
    Hint: Make a joint probability distribution table.
    E(Y1 + 2Y2) = E(Y1) + 2E(Y2) and V(Y1+2Y2) = V(Y1)+4V(Y2)+4Cov(Y1,Y2).

    (b) Find the conditional mean and variance of Y2, given Y1 = 2.
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  2. #2
    MHF Contributor matheagle's Avatar
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    fill in that 2 by 2 table and calculate the means and variances
    There are only 4 possibilities.
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  3. #3
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    Im still a little confuse about using the equation to the table.
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  4. #4
    MHF Contributor matheagle's Avatar
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    I don't like these f's when dealing with discrete rvs

    f(y1,y2) = (y1 + 2y2)/18, (y1,y2) = {(1,1),(1,2),(2,1),(2,2)}

    should be P(Y_1=a,Y_2=b) = {a + 2b\over 18}

    NOW let (a,b) these four choices {(1,1),(1,2),(2,1),(2,2)}

    Those four probabilities better sum to 1, otherwise..................
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