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Math Help - Conditional Expectation Help

  1. #1
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    Conditional Expectation Help

    Suppose you flip one fair coin and roll one fair six-sided die. Let X be the number showing on the die, and let Y = 1 if the coin is heads with Y = 0 if the coin is tails. Let Z = XY.

    Compute E(Z):

    Am I correct when I do E(Z) = E(X)E(Y) = (3.5)(1/2) = 7/4

    Also, how do i do this?

    Compute E(Z|X = 4)

    Thanks
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  2. #2
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    Quote Originally Posted by theprestige View Post
    Suppose you flip one fair coin and roll one fair six-sided die. Let X be the number showing on the die, and let Y = 1 if the coin is heads with Y = 0 if the coin is tails. Let Z = XY.

    Compute E(Z):

    Am I correct when I do E(Z) = E(X)E(Y) = (3.5)(1/2) = 7/4
    I am guessing X and Y are independent, in which case you are correct.

    Also, how do i do this?

    Compute E(Z|X = 4)

    Thanks
    Given that you rolled a 4, what is the expectation of Z? There are only 2 values Y could take with equal probability, so look at what happens at each. You could look at this as \mathbb{E}[4Y].
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