1. Not finding help here? Sign up for a free 30min 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!

Conditinal Expectation Problem

  1. May 4, 2008 #1
    Given x,y and z are standard normal distributions with mean 0 and standard deviation 1. x,y and z are also statistically independent.

    Find E{x|x+y+z=1}.
     
  2. jcsd
  3. May 4, 2008 #2
    symmetry of x, y, and z. For example, interchanging x and y in E[x| x+y+z=1] to get E[y|y+x+z = 1] doesn't change its value.
     
  4. May 5, 2008 #3
    I am not able to understand what you are refering to. Could you please explain. Thanks.
     
  5. May 5, 2008 #4
    Sure thing... If I understand the problem correctly, it doesn't really matter what the exact distributions of x, y, and z are. It only matters that they are identically distributed. Also, note that the condition x+y+z = 1 is unchanged by permuting the letters x,y,z. This, together with their being identically distributed means that

    E{x|x+y+z=1} = E{y|x+y+z=1} = E{z|x+y+z=1}


    Also, think about what E{x+y+z|x+y+z=1} would be, and remember the additive property of the expected value.

    edit: think simple. no hard integrals needed, which was the first thing that came to my mind when I read the problem.
     
    Last edited: May 5, 2008
  6. May 6, 2008 #5
    I left something out....it is also important that x,y,z are statistically independent. If, for example, x and y were statistically dependent, but x and z were not, then that would create an asymmetry and you could no longer conclude that the expected values of x, y, and z were equal.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Conditinal Expectation Problem
  1. Expected value problem (Replies: 3)

  2. Expectation problem (Replies: 3)

Loading...