# Math Help - Trinomial Distribution

1. ## Trinomial Distribution

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

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

I'm asked to find various things, such as

$E(X)$

$E(Y)$

$\text{Var}(X)$

$\text{Var}(Y)$

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

and $\rho$

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

I'd appreciate any input!!

--Chris

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

--Chris