Suppose that

is normally distributed with mean 0, and unknown variance

. Using the method of moment generating functions, show that

has a

distribution with 1 df.

I know that the mgf of a normal distribution is

, so if I was to replace the variable with what was given in the question then I would get:

which looks nothing like the mgf of a

distribution.

Mr F says: You need to stop thinking like this. You **cannot** just substitute like it's a change of variable. This is a grave mistake that is a common to a lot of your solutions. Mr F quarantines the above. ---------------------------------------------------------------------------------------------
the other way I was thinking of doing solving this was using the definition, so I would get:

Mr F says: Good move! Mr F says: NO! When you multiply exponentials with the same base, you ADD the powers (this is a basic index law). You do not multiply the powers.
at which point I don't know how to proceed