Chapter 4.2, Problem 4E

Let X and Y have a trinomial distribution with parameters $n=3,P_x=\frac{1}{6},$ and $P_Y=\frac{1}{2}$.

Find

(a) E(X).

(b) E(Y).

(c) Var(X).

(d) Var(Y).

(c) cov(X,Y).

(f) p

Note that $\rho =-\sqrt{\frac{p_X{p}_Y}{\left(1-p_X\right)\left(1-p_Y\right)}}$ in this ease. (Indeed, the formula holds in general for the trinomial distribution: see Example 43-3.)