I'll do 2, since I mentioned that in class last week
Here you have a Poisson and your mean is a.
You calculate the mean via the Taylor Series for
Let and you have
IN ORDER to get the variance NOTE that we need the second moment
BUT it's easier to get which is NOT the variance.
NOW do the same thing I did above with this and it's over...
NOW let and you have
Add this up and the variance is a.