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    Arrow help with convergence in probability




    If Xn->X (in probability) and Yn->Y(in probability) and Cn=Xn+Yn and C=X+Y show that Cn->C (in probability).

    what i got so far
    |Xn-X|<=ε/2 and |Yn-Y|<=ε/2
    |(Xn+Yn)-(X+Y)|=|Xn-X+Yn-Y|<=|Xn-X|+|Yn-Y|<=ε/2+ε/2=ε


    |(Xn+Yn)-(X+Y)|<=ε
    |Cn-C|<=ε
    so lim(n->inf) P(|Cn-C|>=ε)=0

    I want to verify if this is correct, and if not, what's the mistake, or if I am missing anything.

    Thanks

  2. #2
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    Re: help with convergence in probability


    Your Logic is right.
    In the long run, we're all dead.

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