Quantiles/Order Statistics

statmajor · #1 $Old$ November 5th, 2009, 07:28 PM

Find the smallest value of n for which $P(Y_1 < \xi_{0.5} <Y_n) >= 0.99$ where Y1<...<Yn are the order statistics of a random sample of size n, from a distribution of the continious type.

$\Sigma _nC_m 0.5^n = 1 - 2(0.5)^n >= 0.99; 0.01>= \frac{1}{2^{n-1}}; n = 8$

This example is in my textbook, but I don't get the answer. Would someone be able to briefly explain the steps? Thank you.

matheagle · #2 $Old$ November 6th, 2009, 12:09 AM

and is $\xi_{0.5}$ the median?

statmajor · #3 $Old$ November 6th, 2009, 06:27 AM

I believe so, yes.