We are to solve this problem using mgf. technique (transforms of rv)

x1= b(4,1/2) and x2= b(6,1/3), They are independent.

Let Y = X1+X2

We are looking for the mean and variance.

I assume that we need to proceed as follows:

My(t) = E(e^tY) = ....= E(e^tx1)E(e^tx2).

So I get (1/2 + 1/2 * e^t)^4 * (2/3 + 1/3 * e^t)^6

Now I stuck. Dont i need to create an mgf I recognize (binomial I imagine) and pick out the mean and variance from the mgf parameters?

Help?