1. a. E(Y) = 2.7

b. E(Y2) = 8.1

c. E(2Y + 1) = 6.4 using both the table and the formula.

d. VAR(2Y + 1) = 3.24 using both the table and the formula.

2. a. E(X) = 11

b. E(X2) = 135

c. E(3X − 2) = 31 using both the table and the formula.

d. VAR(3X − 2) = 126 using both the table and the formula.

3. a. E(2Z − 3) = 3

b. VAR(2Z − 3) = 8

c. SD(2Z − 3) = 2.83 (to 3 s.f.)

4. (i) 

(ii)

w
12
18
24
P(W = w)
5 / 18
5 / 9
1 / 6

E(W) = $17.33
VAR(W) = $15.55

(iii)

Z = W − 16

E(Z) = $1.33

VAR(Z) = $15.55

(iv) To be a fair game E(Z) = 0 that is no profit

Because E(Z) = 1.33 the game is not fair and the player has the advantage.

5. a. E(2X + 5) = 9

b. VAR(2X + 5) = 12