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: Ch 7 problem 4 sheldon ross

  1. Mar 6, 2015 #1
    1. The problem statement, all variables and given/known data
    Let X and Y be independent random variables, both being equally likely to be any of the numbers 1, 2, ..., m. Show that E[(absolute value(X-Y))] = ((m-l)(m+1)) / 3m.

    2. Relevant equations

    None, I guess

    3. The attempt at a solution

    Okay so for sample space, since x and y can be any m; total possible combinations are m*m....and then, wasn't really sure where to go....tried talking through bunch of ideas with friends, but....to no avail.
  2. jcsd
  3. Mar 6, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper

    I'd suggest you start by working through the cases explicitly with small numbers. m=1 is no challenge. It's just 0 for the expectation value. m=2 is a little better, you've got the 2^2 cases 1,1 1,2 2,1 2,2. What's the expectation value? Does it match the formula? Now try m=3. Arrange the cases in a square matrix and see if you can think of something to do.
  4. Mar 7, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Much of Ross' book emphasizes a "conditioning argument", and this is one case where you can profitably use that approach:
    [tex] E |X-Y| = \sum_{j=1}^m E\left( |X-Y|\; | Y = j \right) P(Y = j) = \sum_{j=1}^m E |X-j| \, P(Y=j) [/tex]
    The somewhat unfortunate notation ##E(|X-Y| |Y=j)## means ##E(g(X,Y)|Y=j)##, where ##g(X,Y) = |X-Y|##.
    Last edited: Mar 7, 2015
  5. Mar 10, 2015 #4
    Okay, cool, I'll give it a shot.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted