Thread: Normal and Chi-square distribution

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

yes

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?

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.

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.

yep