I am trying to understand transforming random variables into a different distribution. I don't get how this works. Let's say X is normally distributed. We have some function Y = g(X) that transforms X into a variable that is distributed differently.
How would this happen? Unless we square X or something like that, each X would lead to a unique Y, with densities equal to whatever the density of X was. I am not understanding how we could transform X into another distributed random variable, and one that is known.
I'm doing homework and it wants me to transform X to a uniform distribution. Conceptually, I don't understand how this works. Let's say X comes from norm(0, 1). No matter what function g(X) is, I'd imagine Y = g(0) will occur more times than Y = g(5). I'm not understanding what exactly needs to be transformed. Are we trying to transform the density itself - like flatten the density function out?