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Chi-square to standard normal distribution

  1. Oct 3, 2004 #1
    Hi, I have a question

    If X1,X2,...,Xn are independent random variables having chi-square distribution witn v=1 and Yn=X1+X2+...+Xn, then the limiting distribution of

    (Yn/n) - 1
    Z= --------------- as n->infinity is the standard normal distribution.

    I know that Yn has chi-square distribution with v=n, but how to proceed.
  2. jcsd
  3. Oct 4, 2004 #2
    Not given this much thought but ....

    Now since u know Y is Chi-Square Variate with df = n
    What is MGF of Y?
    what is MGF of Z?
    (Note : write MGF of Z in terms of MGF of Y .... i think that should be possible)
    now take limit as n->oo
    see if the MGF of Z is same as that of MGF of a standard normal distribution
    then uniqueness theorem takes over and we are finished ...

    -- AI
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