Find maximum number of ind. r.v. that follows distribution F

[BearY]

Sorry for the abbreviation in the name, the title has a length limit.

Homework Statement

Let X be a r.v. with cumulative distribution function F(x) and density f(x) = F'(x). Find the probability density function of
a) the maximum of n independent random variables all with cumulative distribution function F(x).
b) the minimum of n independent random variables all with cumulative distribution function F(x).

Homework Equations

$F_X(x) = P(X<x)$

The Attempt at a Solution

I know I should have something before I ask the question here, but I have no clue what the question is talking about. Why is there a maximum number of $X$ so that $X\sim F$ for all $X$ to begin with?

 

[StoneTemplePython]

A few thoughts to get you going:

1.) I keep reading the title as referring to max number of indicator random variables... but ind actually seems to mean independent.
2.) Are you sure you have your CDF formula right? Almost everywhere these days its $F_X(x) = P(X\leq x)$ though I understand this is a convention.
3.) I'd ignore PDFs for now. my reading is (a) wants the CDF for the maximum value over n iid r.v.'s and (b) want the CDF for the minimum value over n iid r.v.'s.

To the extent I understand the problem, typically the purposes is to impress upon you the value of working with CDFs and how to manipulate them. That's the thinking part. (Your problem statement says your CDF is differentiable, so you can do that at the end.)

 

[BearY]

A few thoughts to get you going:

1.) I keep reading the title as referring to max number of indicator random variables... but ind actually seems to mean independent.
2.) Are you sure you have your CDF formula right? Almost everywhere these days its $F_X(x) = P(X\leq x)$ though I understand this is a convention.
3.) I'd ignore PDFs for now. my reading is (a) wants the CDF for the maximum value over n iid r.v.'s and (b) want the CDF for the minimum value over n iid r.v.'s.

To the extent I understand the problem, typically the purposes is to impress upon you the value of working with CDFs and how to manipulate them. That's the thinking part. (Your problem statement says your CDF is differentiable, so you can do that at the end.)

Yes, about 1 and Yes less than or equal to is the formal form of cdf on my text as well.
And after seeing your interpretation, my original idea doesn't make any sense to me anymore since it said the maximum of "n random variables" not maximum of n.