POINT ESTIMATION
EXAM TYPE QUESTION
A random sample of x1,x2,.....,xn is taken from a population, which has the probability function F(x) and the density function f(x). The values in the sample are arranged in order and the minimum and maximum values xmin and xmax are recorded.
(i) Show that the distribution function of X max is [F(x)]^n.
Sol.
Consider the value of Xmax. This is will be less than some value x, say, if and only if all the sample values are less than x (Pretty obvious). The probability of this happening is just [F(x)]^n.
How did the notes arrive at this conclusion?
Awaiting reply for both queries. Thanks
Last edited by a moderator: Jul 24, 2011