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

so

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.