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Uniform distribution find E(Y|x)

  1. Apr 2, 2009 #1
    This is the question:

    If X and Y have a uniform distribution over the circle x^2 + y^2 [tex]\leq[/tex] 9 find E(Y|x).

    Can someone please explain to me, how to answer this question. You guys don't have to give me a solution, but a hint would be nice because I have no idea where to start. Thank you :smile:
  2. jcsd
  3. Apr 2, 2009 #2
    well what i was thinking was that the range is between 3 and 0 and -3 and 0.

    Then you integrate x^2 + y^2 with the first range (3 and 0) and then with -3 and 0. Is this right?

    Or is the first range y to 3, and then -3 to 0?

    I have no idea, please help me
  4. Apr 2, 2009 #3


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    "E(y|x)" means the mean value of y for a single value of x. There will only be an integral with respect to y, not x. x is fixed. y ranges between [itex]-\sqrt{9- x^2}[/itex] and [itex]\sqrt{9- x^2}[/itex]. Your final answer for E(y|x) will be a function of x.
  5. Apr 11, 2009 #4
    Thank you for replying. Yupp I think that i got the answer. I got zero at the end, but I'm pretty sure that's right
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