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## Main Question or Discussion Point

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