How to Determine the Transforming Function g(.) from PDFs and CDFs?

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EngWiPy
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Hello,

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

[tex]Y=\,g(X)[/tex]

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

Thanks in advance
 

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S_David said:
Hello,

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

[tex]Y=\,g(X)[/tex]

Now, given that we have the Probabililty Density Function (PDF) of both RVs: [tex]f_Y(y)\mbox{ and }f_X(x)[/tex], 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.
 
bpet said:
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?