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Math Help - plz help in finding Expectation and Covariance

  1. #1
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    plz help in finding Expectation and Covariance

    Finding 6 coins in his pocket, Aloysius proposes a game of chance. He will toss all 6 coins; let X denote the number of heads obtained. Persephone will then toss all the coins which came up tails when Aloysius tossed them. Let Y denote the number of heads Persephone obtains.

    1)Calculate the expectation of Y.
    2)Write down the conditional probability function of X given that Y = 3.
    3)Explain why you would expect the covariance between X and Y to be negative.
    4)Calculate Cov(X, Y) and ρX,Y.
    5)Persephone will pay Aloysius 1 for every Head Aloysius manages to obtain; Aloysius will pay Persephone 2 for every Head Persephone gets. Let Z represent Aloysius' net profit from one game. Calculate the expectation and variance of Z
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by goaway716 View Post
    Finding 6 coins in his pocket, Aloysius proposes a game of chance. He will toss all 6 coins; let X denote the number of heads obtained. Persephone will then toss all the coins which came up tails when Aloysius tossed them. Let Y denote the number of heads Persephone obtains.

    1)Calculate the expectation of Y.
    2)Write down the conditional probability function of X given that Y = 3.
    3)Explain why you would expect the covariance between X and Y to be negative.
    4)Calculate Cov(X, Y) and ρX,Y.
    5)Persephone will pay Aloysius 1 for every Head Aloysius manages to obtain; Aloysius will pay Persephone 2 for every Head Persephone gets. Let Z represent Aloysius' net profit from one game. Calculate the expectation and variance of Z
    Label the coins 1 to 6, the probability p_i that P gets a head with coin i is that came up tails for A and heads for P, that is p_i=1/4.

    So the number of heads that P gets from the 6 initial coins Y\sim B(6,1/4)

    CB
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