Re: function of random variables

given random variables X and Y with a joint density:
1/2pi * exp(-(x²+y²)/2)
find the density function of Z=X/(sqrt(X²+Y²))

I know I have to find the area in which x/sqrt(x²+y²)
<= z and integrate the density function over this
area but I can't really find it.



X and Y are independent and are each N(0,1).

Z = +/- 1/sqrt(1+y^2/x^2),

where y^2/x^2 ~ F(1,1) = t(1)^2 = Cauchy^2.

Use the fact that Z is positive with probability 1/2 and negative with probability 1/2.

Jack
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