I've been struggling with this particular distribution. I'm told that $\displaystyle X$ and $\displaystyle Y$ have a trinomial distribution with parameters $\displaystyle n=3$, $\displaystyle p_1=\tfrac{1}{6}$ and $\displaystyle p_2=\tfrac{1}{2}$

I know that the joint pmf is $\displaystyle f(x,y)=\frac{6}{x!y!(3-x-y)!}\left(\tfrac{1}{6}\right)^x\left(\tfrac{1}{2}\ right)^y\left(\tfrac{1}{3}\right)^{3-x-y}$

I'm asked to find various things, such as

$\displaystyle E(X)$

$\displaystyle E(Y)$

$\displaystyle \text{Var}(X)$

$\displaystyle \text{Var}(Y)$

$\displaystyle \text{Cov}(X,Y)$

and $\displaystyle \rho$

I don't want anyone to solveallof these.

However, if someone can show me how to find the expected value of either x or y, I would be able to figure out the rest.

I have an inkling that $\displaystyle E(X)=\mu_x=\sum_{x} xf_X(x)$, but how would I find the marginal of $\displaystyle X$???

I'd appreciate any input!!

--Chris