Results 1 to 2 of 2

Math Help - convergence of random variables

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    26

    convergence of random variables

    Suppose X_{n} \rightarrow X in probability and X_{n}^{2} \le W, \forall n where E(W) is finite. Show X_{n} \rightarrow X in mean square.

    So far I have:

    E((X_{n}-X)^2)=E(X_{n}^{2})-2E(X_{n}X)+E(X^{2})<br />
\le E(W)-2E(X_{n}X)+E(X^{2})

    I'm not even sure if I'm on track or not. I can't think of how to use the convergence in probability to get anywhere.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Are you sure that it's X_n^2\leq W ?
    Have you studied Lebesgue's dominated convergence theorem ?

    Yuck, this problem sucks !
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. convergence of random variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 14th 2011, 01:22 AM
  2. convergence problem on random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 21st 2010, 03:31 PM
  3. Convergence of random variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 25th 2009, 11:25 AM
  4. Convergence of random variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 16th 2009, 02:21 AM
  5. Convergence of sequence of continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: September 18th 2009, 08:25 AM

Search Tags


/mathhelpforum @mathhelpforum