convergent in absolute value but not in quadratic mean

Discussion in 'Probability' started by quebecstat, Jan 17, 2008.

  1. quebecstat

    quebecstat Guest

    Hi everybody,

    I would like to find a random variable Yn that converges in absolute
    value (to c), ie E|Yn-c| goes to 0 when n goes to infty,

    but not in quadratic mean, ie E(Yn-c)^2 does not go to 0 when n goes
    to infty

    Thanks for your help.
     
    quebecstat, Jan 17, 2008
    #1
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  2. quebecstat

    tommy.mielke Guest

    X_n := 1_[0,1/n] \sqrt(n)

    then E|Xn - 0| = \sqrt(n) / n -> 0

    but E|X_n - 0|^2 = 1
     
    tommy.mielke, Mar 16, 2008
    #2
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