Probability of a Min/Max I am studying probability for an exam and I am finding hard to understand the notion of $P(\min(X_1,X_2))$ and $P(\max(X_1,X_2))$, where $X$ is a discrete or a continuous variable.
I have found in my book that $P(\min(X_1,X_2)>t) = P(X_1>t)\cdot P(X_2>t)$ and $P(\max(X_1,X_2)\leq t) = P(X_1\leq t)\cdot P(X_2\leq t)$. Could you explain (or link) me what is the theory behind it? 
Thank you very much

There's not really any probability or algebra involved here, it's just a question of logic.  Saying that $\min(X_1,X_2)>t$ is just the same as $X_1>t$ and $X_2>t$, because if the smaller one is greater than $t$ then the other one must be too.
Hence
$$P(\min(X_1,X_2)>t)=P(X_1>t\ \hbox{and}\ X_2>t)\ ,$$
and if you have suitable independence properties this is
$$P(X_1>t)\,P(X_2>t)\ .$$
