1 Suppose that we have a box with 3 white marbles 3 green ma

1) Suppose that we have a box with 3 white marbles, 3 green marbles, and 3 red marbles in it. We choose three marbles without replacement from the box and let W = the number of white marbles chosen and G =the number of green marbles chosen.

(a) Calculate the Var(W).

(b) Calculate the Cov(W, G).

Solution

W=the number of white marbles chosen and we have choose three marbles

(a)

E(W)=0.2389*0+0.535*1+0.214*2+0.012*3=1

E(W²)=1.5

Var(W)=1.5-1=0.5

(b)

E(G)=0.535*1+0.214*2+0.012*3=1

Cov(W,G)=E(W,G)-E(W)E(G)

The possible outcomes is (W,G,R)

(1,1,1),(1,2,0),(1,0,2),(2,0,1),(2,1,0),(3,0,0),(0,3,0),(0,0,3),(0,1,2),(0,2,1)