1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Order statistics in the uniform (probability) distribution

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi there: I just need someone to tell me if I've made a mistake somewhere in my solution to this:

    Suppose that X1 , . . . , X2n+1 are i.i.d. random variables that form a random sample
    from the U (0, 1) distribution. Suppose that the values are arranged in increasing order as
    Y1 ≤ Y2 ≤ . . . ≤ Y(2n+1) . Calculate expressions for the distribution function and for the probability density function of the random variable Y(n+1) (the sample median).

    3. The attempt at a solution
    Now if we want Y(n+1) to be in the interval [a,b] we need to have exactly n of the Xi in [0,a] and n+1 in [a,1], but ensure not all of the latter n+1 are in [b,1]. So we have [itex]{{2n+1}\choose{n+1}}a^n[(1-a)^n-(1-b)^n][/itex] where the [itex](1-a)^n-(1-b)^n[/itex] ensures not all n+1 of the latter Yi are in the [b,1] interval. But shouldn't there be some sort of symmetry in a and b with this function: shouldn't it be F(b)-F(a) where F'(x) is the pdf of the question? Because it doesn't look much like an F(b)-F(a) to me...

    Thanks a lot,

  2. jcsd
  3. Mar 22, 2009 #2
    Anyone? Any help would be very much appreciated, no matter how small!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook