This might be a very basic level question. I am dealing with independent and identically distributed (i.i.d) random variables, but got stuck in the following step:
$$P = A \underset{1\leq n\leq N}{\operatorname{max}} |X_n|^2 \tag 1$$
where $X$ is some random variable, $A$ is some constant. Also, the PDF of |X| is know and for simplicity I denote it by $f_X(x)$.
My query is, can we write eq.(1) as
$$P = A \{[f_X(x)]^2\}^N \tag 2$$
I mean to say can we square the PDF as done in eq. (2).
Any help in this regard will be highly appreciated.