r.v. Law of the min On a probability space $(\Omega, A, P)$, and given a r.v. $(X,Y)$ with values in $R^2$. If the law of $(X,Y)$ is $\lambda \mu e^{-\lambda x - \mu y } 1_{R^2_+} (x,y) dx dy$, what is the law of the min $(X,Y)$?

HINT 
Let $Z=\min(X,Y)$. Start by computing, for some $z>0$ 
$$
   1-F_Z(z) = \mathbb{P}\left(Z>z\right) = \mathbb{P}\left(X>z, Y>z\right)
$$
Notice that the probability of $(X,Y)$ factors, i.e. $X$ and $Y$ are independent, hence
$$
   \mathbb{P}\left(X>z, Y>z\right) = \mathbb{P}\left(X>z\right) \mathbb{P}\left(Y>z\right)
$$
