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