# Is it possible to obtain joint PDF of set of variables given marginal PDF of each variable?

Say $f(X_1)$, $f(X_2)$, $f(X_3)$, $f(X_4)$ are the empirical marginal PDFs of random variables $X_1$, $X_2$ , $X_3$, $X_4$. Also given is correlation between each pair of variables $X_1$, $X_2$ , $X_3$, $X_4$. Is it possible to obtain the empirical joint PDF of $f(X_1, X_2, X_3, X_4)$?

• How do you define "empirical marginal PDFs"; – JohnK Jul 9 '16 at 17:08
• @JohnK I obtained empirical PDFs from an experiment that I conducted – Spandyie Jul 9 '16 at 17:11
• not without additional assumptions (eg. multi-variate normality would be sufficient). – Matthew Gunn Jul 9 '16 at 17:28