The transformation of a random variable is well documented and there are numerous examples on the web. Most examples present univariate variable transformation utilising inverse of the transformation function. The method works whenever the transformation function is one-to-one.(adsbygoogle = window.adsbygoogle || []).push({});

Let's say g(x)=x^2 such that x>=0.

I am interested in solving a problem when the transformation function is not a monotone function ie not one-to-one on an interval.

For example, I have two random variables X and Y. X variable has a probability density function f(x)=0.2e^(-x/5) x>0, this is pdf of a classical exponential probability distribution. And a simple linear transformation function Y=3X for X>5 otherwise Y=7 when 0<X[tex]\leq5[/tex]

Clearly, on [0, 5) g(.) transformation is not one-to-one. Would be possible to find pdf or cdf of variable Y only on (5,inf) or can it be determine over (0, infinity)?

Thanks!

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# Transformation of a random variable

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