Results 1 to 3 of 3

Math Help - Independence of random variables X and X^2

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    2

    Independence of random variables X and X^2

    If we have two r.v.: X = { -1, 0, 1 } and Y= X^2, with X uniformly distributed with probability 1/3, then X and Y are independent, right?

    Pdf values of Y are 2/3 if Y=1 and 1/3 if Y=0.
    I can construct joint pdf with f(x, y), such that f(i, -1) = 0, f(i, 0) = 1/9 and f(i, 1) = 2/9. Then for every f(i, j), f(x, j) = f(x)f(y), and that is the definition of independence.

    Am I missing something?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

    Re: Independence of random variables X and X^2

    Saying Y=X^{2} and 'X and Y are independent' is 'a little contradiction'... isn't it?...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2011
    Posts
    2

    Re: Independence of random variables X and X^2

    Yes, I have just understood that X's and Y's cannot be chosen independently.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Independence of Random Variables
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 18th 2011, 07:39 PM
  2. Replies: 6
    Last Post: November 16th 2009, 02:42 PM
  3. Proof of independence of random variables
    Posted in the Advanced Statistics Forum
    Replies: 10
    Last Post: September 28th 2009, 12:31 PM
  4. stochastic independence and random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 4th 2008, 11:12 PM
  5. 3 Gaussian random variables, independence
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 12th 2007, 04:06 AM

Search Tags


/mathhelpforum @mathhelpforum