00:01
All right, so we have a situation where we have x1 all the way up to xn, our normal 0 sigma squared, their iid, and we define v sub n equal to 1 over n, the sum of the x sub i squared.
00:20
All right, so this would remind you of a chi -squared distribution.
00:22
Recall that the chi -squared distribution with k degrees of freedom is the result of summing these squares of k standard unit normals.
00:32
All right, so the key to kind of think about this is just rewrite it a little bit.
00:35
All right, we know that in this case x1 over sigma is going to be, sorry, over x1 over sigma squared will result in a normal 0, 1, right? so xi over sigma squared is really normal 0, 1.
00:58
So in general, this means that if we just sum these guys up, we sum from i equals 1 to n of x sub i over sigma squared, this thing would be chi -squared with n degrees of freedom distributed...