Question

Let X and Y have a trinomial distribution with parameters n = 3, px = 1/6, and Py = 1/2. Find (a) E(X). (b) E(Y). (c) Var(X). (d) Var(Y). (e) Cov(X, Y). (f)p

Answer 1

The expected value of X is 1/2, the expected value of Y is 3/2, the variance of X is 5/12, the variance of Y is 3/4, the covariance of X and Y is -1/4, and p is -√(3/5).

Step-by-step explanation:

(a) E(X) = npx = 3 * (1/6) = 1/2

(b) E(Y) = npy = 3 * (1/2) = 3/2

(c) Var(X) = npx(1-px) = 3 * (1/6) * (5/6) = 5/12

(d) Var(Y) = npy(1-py) = 3 * (1/2) * (1/2) = 3/4

(e) Cov(X, Y) = -npxpy = -3 * (1/6) * (1/2) = -1/4

(f) p = Cov(X, Y) / √(Var(X) * Var(Y)) = (-1/4) / √((5/12) * (3/4)) = -√(3/5)