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Let $X_n$ a random variable of same law

  1. Sep 14, 2004 #1
    :confused: Hello

    I have a simple question :
    Let $X_n$ a random variable of same law
    If $V(X_n)\longrightarrow 0$ when $n\longrightarrow +\infty$
    How schow that : $E(X_n)\longrightarrow C$ and $E(X_{n}^{2}\longrightarrow C^2$ and C is a constant?
    Thanks
     
  2. jcsd
  3. Sep 14, 2004 #2
    Hello

    [tex]

    I have a simple question :
    Let $X_n$ a random variable of same law
    If $V(X_n)\longrightarrow 0$ when $n\longrightarrow +\infty$
    How schow that : $E(X_n)\longrightarrow C$ and $E(X_{n}^{2}\longrightarrow C^2$ and C is a constant?
    Thanks
    [/tex]
     
  4. Sep 14, 2004 #3
    Feynman, LaTex is down at the moment.
     
  5. Sep 15, 2004 #4

    uart

    User Avatar
    Science Advisor

    How far have you got with this one Feynman?

    I suggest you let z = x - E(x) and then prove that E( z^2 ) = 0 implies that Z has a discrete probability denstiy with P(z=0) = 1.
     
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