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Math Help - probability theory

  1. #1
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    probability theory

    Hi guys!

    Can you help me with this:

    Let Y be a random variable taking values 0 and 1 with probability 0.5
    each. Find expected values of random variable Z = XY
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  2. #2
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    Re: probability theory

    Hey nstockholm.

    What is X? Is it a constant or random variable? What is its distribution (if its a random variable)?
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  3. #3
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    Re: probability theory

    probability theory-porblem.png

    here is the whole problem , I solved 2a but 2b I don't know
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  4. #4
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    Re: probability theory

    probability theory-porblem.png

    here is problem
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  5. #5
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    Re: probability theory

    If X and Y are independent then E[XY]=E[X]\times E[Y]
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  6. #6
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    Re: probability theory

    ok? but what happen then ?
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  7. #7
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    Re: probability theory

    Hi nstockholm,

    I think the issue might be this: The problem asks you to find the expected values of Z and their probabilities, not the expected value of Z. This is probably a poor choice of words. It would be better to call them possible values or something like that.

    It is clear that the possible values of Z are the same as those of X, since multiplying with Y means multiplying by either 0 or 1. Can you find the new probabilities?
    Last edited by TwoPlusTwo; September 26th 2013 at 10:35 AM.
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  8. #8
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    Re: probability theory

    Form the joint distribution using independence P(A = a, B = b) = P(A = a)P(B = b) and calculate the expectation (you can also use Shakarri's hint above which will give you the exact same answer).
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