Let $X \sim N(\mu_1, \sigma_1)$, $Y \sim N(\mu_2, \sigma_2)$, $Z \sim N(\mu_3, \sigma_3)$. I want to derive a joint distribution for $X/(X+Y+Z)$ and $Y/(X+Y+Z)$.
Since two random variables i.e. $X/(X+Y+Z)$ and $Y/(X+Y+Z)$ are dependent, I can not simply multiply them. So, how the pdf or cdf of their joint can be derived??
I do appreciate your answers.