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Math Help - Basic expectation question

  1. #1
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    Basic expectation question

    Assign a value of 1 point to an Ace, 11 points to Jack, 12 to a Queen, and 13 for a King. The numbered cards (2-10) are assigned the value shown on the card.

    Draw 2 cards with replacement.

    Let X be the value of the first card, and let Y be the value of the second card. What is E(X+Y)? StdDev(X+Y)?

    Is it E(X+Y) = E(X) + E(Y) = 14?

    E[(X+Y)^2] = ??

    Also, is the distribution of X, P(X=x ) = 4/52?

    Thanks !
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  2. #2
    MHF Contributor matheagle's Avatar
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    P(X=k)=1/13 for k=1,2,3... 13 same for Y.
    They are indep.

    So compute E(X) and E(X^2)....

    By indep, since you are sampling wr, we have V(X+Y)=V(X)+V(Y)
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