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Random Variable Transformation

  1. Jan 24, 2010 #1
    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
     
  2. jcsd
  3. Jan 24, 2010 #2
    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.
     
  4. Jan 25, 2010 #3
    Ok, then?
     
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