Chapter 10 Exam Type Question

[ldr]

Hello

I’m having difficulty of understanding the concept of the XMAX XMIN question on chapter 10 page 33 of CT3.

I sort of understand the concept of XMAX and how is is essentially F(x) and because their are n in the sample then distribution function is F(x)^n

For XMIN in the solution sections it explains how it is the opposite of XMAx so (1-F(X))^n I just don’t understand why it then becomes 1-(1-F(X))^n. The 1- at the beginning confuses me

Any help understanding this concept will be hugely appreciated

Thanks

 

[John Lee]

(1-F(X))^n gives [P(X>x)]^n = P(Xmin > X)

But we want the CDF of Xmin, hence we want P(Xmin <x) and thus we need the 1-