# Transformation of random variable

#### Dhamnekar Winod

##### Active member
Hello,

A discrete random variable X takes values $x_1,...,x_n$ each with probability $\frac1n$. Let Y=g(X) where g is an arbitrary real-valued function.

I want to express the probability function of Y(pY(y)=P{Y=y}) in terms of g and the $x_i$
How can I answer this question?

The notation Y(pY(y)=P{Y=y}) is confusing. For one, $Y$ accepts as argument elements of $\{x_1,\ldots.x_n\}$ and not equalities. if you need the probability mass function of $Y$, it is $$\displaystyle f_Y(y)=|g^{-1}(y)|/n$$. I don't think this can be simplified unless we know more about $g$.