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Assume an x-coordinate from the unit circle is picked from a uniform distribution.

This is the outcome of the random variable X with probability density function Xden(x) = 0.5 (-1 < x < 1).

The random variable Y is related to the random variable X by Y = f(X) = √(1-X

^{2}) and X = g(Y) = ±√(1-Y

^{2}).

What is the probability density function Yden(y)?

Since Yden(y) = Xden(g(y)) / |f'(g(y))|, i first calculate f'(x) = -x/√(1-x

^{2}).

Then Yden(y) = Xden( √(1-Y

^{2}) ) / f'( √(1-Y

^{2}) ) + Xden( -√(1-Y

^{2}) ) / f'( -√(1-Y

^{2}) )

I get Yden(y) = 0

Where do i go wrong?

Rgds

Rabbed