Results 1 to 2 of 2

Math Help - probability convergence

  1. #1
    Senior Member
    Joined
    Sep 2009
    Posts
    299

    Exclamation probability convergence

    Show that Xn->0 (in probability) iff |Xn|->0 (in probability).

    What i have so far
    |Xn|->0 (in probability) iff for any ε>0 P(||Xn|-ε|>=0)->0 as n->inf. But P(||Xn|-ε|>=0)=P(|Xn|>=ε)=P(|Xn|>=0)=P(|Xn-ε|>=ε) so this is true iff Xn->0 (in probability)

    Is this logic correct?
    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,

    You misused the definition of convergence in probability.

    |X_n|\to X iff P(||X_n|-X|>\epsilon)\to 0
    So here it gives P(|X_n|>\epsilon)\to 0

    If you try to write it, this is exactly the definition of X_n converging in probability to 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence in probability but no convergence in L^p nor A.S.
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 16th 2011, 05:17 AM
  2. Convergence in probability
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: January 30th 2011, 06:12 PM
  3. Convergence in probability
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: January 17th 2011, 08:48 AM
  4. fundamental in probability & convergence with probability 1
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 23rd 2010, 09:58 AM
  5. Almost sure convergence & convergence in probability
    Posted in the Advanced Statistics Forum
    Replies: 9
    Last Post: November 27th 2009, 11:31 PM

Search Tags


/mathhelpforum @mathhelpforum