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