Random Variable Transformation

[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.

Thanks in advance

 

[bpet]

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.

Thanks in advance

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.

 

[EngWiPy]

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.

Ok, then?