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Expected value of a semicircle

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Point is chosen at random (uniform PDF) within semi-circle: {(x,y)|x2+y2≤r2, y≥0}

    Basically, I'm supposed to find E[X] for this problem

    2. The attempt at a solution

    I know how to do it, in a very long-winded fashion
    (find fY(y), and E[X|Y=y] etc).
    But my teacher says that there is an easier way that doesn't involve a lot of calculations, anyone see it?
    Thanks

    EDIT;;;;

    I think i might have gotten it, because the semicircle is an even function, the expected value of the first moment is 0. Can someone confirm this also?
    Also, does this apply to a regular circle as well?
     
    Last edited: Oct 30, 2011
  2. jcsd
  3. Oct 30, 2011 #2

    Stephen Tashi

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    Science Advisor

    That is not a precise statement. What function are you referring to? If you are referring to the equation for the boundary of the semi-circle, that doesn't justify any conclusions about the moment of X.
    You could argue by symmetry if the distribution function that the mean value of X in the semicircle is 0. ( Don't say "expected value of the first moment" because the first moment of X is the expected value of X.)
     
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