+ Reply to Thread
Results 1 to 2 of 2

Thread: Expected value of second highest draw

  1. #1
    Points: 3,818, Level: 39
    Level completed: 12%, Points required for next Level: 132

    Thanked 0 Times in 0 Posts

    Expected value of second highest draw

    Hello all,

    Suppose I take two draws from a uniform distribution on [0,1]. I know that the value of the highest draw is equal to x. What then is the expected value of the second highest draw conditional on the highest draw being x? What is the distribution of the second highest draw (conditional on the knowledge our highest draw is x)?

    Thank you kindly for your help,


  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Thanked 565 Times in 537 Posts

    Re: Expected value of second highest draw

    Let U_1, U_2 \sim {\rm Uniform}(0,1) be the random sample

    Let X = U_{(2)} \geq U_{(1)} = Y be the ordered sample

    Then \forall x \in (0, 1), \forall y \in (0, x],

    F_{Y|X = x}(y|x) = \Pr\{Y \leq y|X = x\}

    = \Pr\{Y \leq y|Y \leq x\}

    = \frac {\Pr\{Y \leq y, Y \leq x\}} {\Pr\{Y \leq x\}}

    = \frac {\Pr\{Y \leq y\}} {\Pr\{Y \leq x\}}

    = \frac {y} {x}

    \Rightarrow Y|X = x \sim {\rm Uniform}(0, x)

+ Reply to Thread


Similar Threads

  1. Replies: 0
    Last Post: 02-15-2011, 06:40 PM
  2. Help with draw of random numbers
    By Peeledseal in forum Probability
    Replies: 3
    Last Post: 01-03-2011, 10:58 AM
  3. Highest numbers
    By math_chick27 in forum SAS
    Replies: 3
    Last Post: 09-07-2010, 10:39 PM
  4. How to draw this graph?
    By chadefa1 in forum R
    Replies: 2
    Last Post: 06-03-2010, 11:04 AM
  5. highest correlation
    By latonya1 in forum Statistics
    Replies: 2
    Last Post: 06-18-2007, 01:32 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts

Advertise on Talk Stats