# Random Variable Transformation

1. Jan 24, 2010

### EngWiPy

Hello,

Suppose that a random variable Y is formed by transforming another random variable X by using the tranforming function g(.). That is:

$$Y=\,g(X)$$

Now, given that we have the Probabililty Density Function (PDF) of both RVs: $$f_Y(y)\mbox{ and }f_X(x)$$, how can we specify g(.)? I didn't give an exact example because I just need to know the procedure.

2. Jan 24, 2010

### bpet

It'll be a bit easier to use the CDFs and assuming g is one-to-one & monotonic:

F_X(x) = Prob(X<=x) etc.

3. Jan 25, 2010

Ok, then?