Results 1 to 1 of 1

Math Help - Joint distribution, conditional distribution

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    43

    Joint distribution, conditional distribution

    \text{Let } Y \sim \mathcal{N}(\mu, 1) \text{ and } X|Y \sim \mathcal{N}(Y, \sigma^2) .
    \mathcal{N} \text{ denotes normal distribution.}
    i) Show that (X, Y) pair has the same joint distribution as the (Y+Z, Y) pair, where Z is a independent standard normal random variable.
    ii) Using i) show that X,Y pair is a two dimensional normal distribution.
    iii) Calculate E(X), Var(X), Corr(X,Y).
    iv) Find E(Y | X=x).
    v) What is the conditional distribution of Y given X=x?

    I would really appreciate if you could help me.
    Last edited by doug; December 4th 2011 at 12:30 AM. Reason: The problem had no sense, I corrected a confusing typo. Sorry!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint Distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 29th 2011, 10:31 AM
  2. one last joint distribution
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: October 28th 2009, 08:42 AM
  3. Conditional distribution and finding unconditional distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: December 2nd 2008, 04:48 AM
  4. joint distribution
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: May 24th 2008, 10:55 PM
  5. joint distribution
    Posted in the Advanced Statistics Forum
    Replies: 8
    Last Post: April 15th 2007, 12:52 PM

Search Tags


/mathhelpforum @mathhelpforum