Let $X$ be a random variable uniformly distributed over $(0,1)$. Assume a random variable $Y=X^n$, where $n$ is a fixed number. Please find the probability density function for the random variable $Y$; i.e., $f_Y (y)$?.
Could anyone point me in the right direction as far as formulas go for this? I'm kind of lost on how to start, and the book I have right now is not helping a single bit.