Minimum of random variables iid I have lots of problems trying to solve problems involving maximum and minimum of random variables. For example:
Let $X_{1},X_{2},...,X_{n}$ random variables iid and $f_{X}(x)= \frac{1}{x^{2}}$ when $x\geq 1$ and $f_{X}(x)=0$ in other case. 
My problem is that I have no idea how to deal with the $Z=min\{X_{1},...,X_{n}\}$, I should be able to find $F_{Z}(z)$ and $f_{Z}(z)$.
Thanks so much in advance for all your help.

The input needed here is the hard-to-immediately-grasp idea that the minimum order statistic exceeding a threshold is equivalent to having all the random variables of the sequence being greater than that threshold for non-negative random variables (such as yours). That is
$$P(Z>z) = P(\min(X_1,X_2,\dots, X_n)>z) = P(X_1>z,X_2 >z, \dots, X_n>z)$$
From here, you could go by finding the cumulative distribution function by using the fact that $P(Z>z)=1-P(Z\leq z)$ and the independence assumption of the sequence. The pdf follows through differentiation.
