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Finding the Probability Density Function

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A dial indicator has a needle that is equally likely to come to rest at an angle between 0 and Pi. Consider the y-coordinate of the needle point (projection on the vertical axis). What is the probability density function (PDF) p(y)?

    2. Relevant equations
    I know the integral of p(y) over all space has to equal 1. The y-coordinate of the dial is of course radius*sine(theta).

    3. The attempt at a solution

    The first part of the question asked for the PDF for the angle, which wasn't too difficult. Knowing the integral over all space had to equal 1 and that the probability was a constant I could see that p(theta)=1/Pi . I just can't find any recipe on how to come up with the PDF for the y coordinate, in most cases it is given! I can see that it must be zero at both y=0 and y=r, which suggests to me it is probably sine or sine^2 but I cannot prove it.

    Thanks a bunch.
    Last edited: Jan 22, 2008
  2. jcsd
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