If X~N(0,1) is X^2~Chisquare(1) ?

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- May 12th 2011, 04:33 AMsupaman5Normal and Chi-square distribution
If X~N(0,1) is X^2~Chisquare(1) ?

- May 12th 2011, 04:35 AMSpringFan25
yes

- May 12th 2011, 04:58 AMsupaman5
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? - May 12th 2011, 05:04 AMSpringFan25
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. - May 12th 2011, 05:08 AMsupaman5
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.

- May 12th 2011, 09:25 AMSpringFan25
yep ;)