The question is:

Let X be a binomial random variable based on n trials, and a success probability of ; let Y be an independent binomial random variable based on m trials and a success probability of . Find E(W) and Var(W), where W=4X+6Y.

(E(W) - expected value of W)

So from what I understand, that means and the probability function for Y is similar.

I also know that given a variable say Z = X + Y, that .

However since I have W=4X+6Y, I thought maybe then it should be something like . However that becomes a really ... nasty expression which I'm not sure how to simplify. I feel like I am doing something wrong.

I should be able to figure out the variance if I can do the expected value, because I should be able to just use the equation for variance.