What Are the PDFs for Transformed Variables in These Probability Distributions?

[jbaum517]

1. If X is normal distributed with E(x) = 0 and V(x) = 16 or N(0,16) if you prefer, and Y = e^X, what is the pdf for Y [f(y)] for 0≤y

2. If X is a Cauchy Distribution: f(x) = 1/(π(1+x^2)) and Y = 1/(X^2), what is the pdf for y

3. Same as #2, but Y = X^2

Any help as well as an explanation would be great. Explanation doesn't have to be long as I feel like I'm close and understand the material fairly well, just need a little help.

Thanks!

 

[Ray Vickson]

Standard method (for #1): P{Y <= y} = P{exp(X) <= y} = P{X <= ln(y)}, so the density of Y is f(y) = (d/dy)P{X <= ln(y)}, which you can evaluate.

The others are similar.

RGV