Let $B(\alpha, \beta)$ denote the Beta distribution with parameters $\alpha$ and $\beta$. What do we know about a random variable $Y \sim cB(\alpha, \beta)$ where $c \in (0, 1)$?
Obviously, $Y$ does not follow a Beta distribution anymore, as the support of the distribution of $Y$ has to be $(0, c)$ now. Does $Y$ have any well-known distribution? Is the density function of $Y$ just ''squeezed'' into $(0, c)$?