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Math Help - Normal and Chi-square distribution

  1. #1
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    Normal and Chi-square distribution

    If X~N(0,1) is X^2~Chisquare(1) ?
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  2. #2
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    yes
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  3. #3
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    Also if X_1,...,X_n ~N(mu,sigma^2)

    is the sum of [((X_i-mu)^2)/sigma^2] ~ chisq(n)

    or is it {the sum of (X_i-mu)^2}/sigma^2 ~ chisq(n)?

    or are these two the same, becasue sigma^2 can be taken outside of the sum?
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  4. #4
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    if you can answer the below, you can answer your own question:

    is "(X-mu)/sigma" distributed as N(0,1) ?



    On the "are they the same" question: yes, provided that sigma is constant for all Xi.
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  5. #5
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    Oh ok, thanks, so chisquare takes its parameter to be the number of variables, and if X_i are not the standard normal distribution, they have to be normalised first.
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  6. #6
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    yep
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