- #1
maverick280857
- 1,789
- 4
Hi
Suppose [itex]X_{1}, \ldots, X_{n}[/itex] is a sequence of i.i.d. random variables. We define
[tex]X_{(n)} = max(X_{1}, \ldots, X_{n})[/tex]
[tex]X_{(1)} = min(X_{1}, \ldots, X_{n})[/tex]
Are [itex]X_{(n)}[/itex] and [itex]X_{(1)}[/itex] independent?
Whats the best/easiest way to verify this?
Thanks
Vivek
Suppose [itex]X_{1}, \ldots, X_{n}[/itex] is a sequence of i.i.d. random variables. We define
[tex]X_{(n)} = max(X_{1}, \ldots, X_{n})[/tex]
[tex]X_{(1)} = min(X_{1}, \ldots, X_{n})[/tex]
Are [itex]X_{(n)}[/itex] and [itex]X_{(1)}[/itex] independent?
Whats the best/easiest way to verify this?
Thanks
Vivek