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!

Showing Chi squared is independent with another variable

  1. Dec 11, 2014 #1
    So I have X1 and X2 are iid standard normal.

    Then I have Y=X1^2+ X2^2

    and

    Z=X1/(X1^2+x2^2)

    I'm supposed to find the distribution of Y and Z and then determine if they are independent.

    Clearly Y is chi squared with degrees of freedom 2.

    But I have no idea how to find the distribution of Z. I know there is a shortcut without using the jacobian, like I did with the Chi Squares, but I'm not sure how to do it.



    I know Y and Z are not independent because with some algebra,

    Y=Y*Z^(2)+X2
    So Y depends on Z and vice versa, therefore they cannot be independent. Is that true?
     
  2. jcsd
  3. Dec 11, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    (I moved this thread to the homework section)

    I could be interesting to go to polar coordinates (in the X1-X2-plane).

    Just finding an equation where Y and Z appear is not sufficient to show a dependence.
    Imagine Y=X1, Z=X2, then Y+Z=X1+X2 but they are clearly independent.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Showing Chi squared is independent with another variable
  1. Chi Squared (Replies: 1)

Loading...