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Worksheet #3 Key
1.
A lottery has four possible payoffs: $1,000 at p= 0.05, $500 at p = 0.15, $100 at p =
0.3, $0 at p = 0.5.
a. Calculate the expected value of the lottery.
EV = $1,000 * 0.05 + $500* 0.15+$100*0.3 = $155
b. Calculate the standard deviation of the outcome of the lottery
VARIANCE = .05(1000155)
2
+.15 (500 155)
2
+ .3(100155)
2
+ .5(0 – 155)
2
=
66475
SD = the square root of VAR = 257.83
c. What would a risk neutral person pay to play this lottery?
$155
2. Suppose state lottery tickets cost $1.00 and the payoffs are as follows:
Probability
Return
0.6
$0.00
0.25
$1.00
0.1
$2.00
0.05
$10.00
a. Calculate the expected value of the lottery.
EV = .6*1 + .1 *1 + .05*9 = .05
b. Calculate the standard deviation of the outcome of the lottery.
Var = 4.74 => SD = 2.178
c. Based on the law of large numbers and the expected value, is this lottery a good
proposition for the state?
Yes, the average payoff is negative, which is a profit for the state.
3. An investor is concerned about a choice of a purchasing a partnership share minor
league baseball team in an independent league. There are four possible outcomes for
average first year profits based on the teams success.
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 Spring '09
 Maxcy

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