# Finding the Probability Density Function

1. Jan 22, 2008

### sarujin

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