
Trinomial Distribution
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 $\displaystyle f(x,y)=\frac{6}{x!y!(3xy)!}\left(\tfrac{1}{6}\right)^x\left(\tfrac{1}{2}\ right)^y\left(\tfrac{1}{3}\right)^{3xy}$
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 solve all of 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!! (Nod)
Chris

nvm....I overcomplicated this. I figured it out.
Chris