|
payoff |
probability |
|---|---|
|
50 |
0.25 |
|
25 |
0.5 |
|
0 |
0.25 |
The table above provides a new gamble. Answer the following 4 questions based on the new gamble.
a.What is the expected payoff of this gamble? Enter the numerical value only.
b.What is the variance of the gamble? Put down the numerical value using one decimal.
c.Suppose the person has a utility over amounts for sure equal to u(y) = square root of y. What is the expected utility of the gamble? Use three decimals in your numeric answer.
d.What is the amount for sure that would give the person the same expected utility as the gamble? Use two decimals in your numeric answer.
a) The expected value of the gambling is = 50(0.25)+25(0.5) = 12.5+12.5 = 25
b) the varience is the sum of the deviation from the mean weighted by their probability :
Varience = 50(0.25 - 25)2+ 25(0.5 - 25)2 + 0 (0.25-25)2 = 50(-24.75)2 + 25(-24.5)2 = 50(612.5)+25(600.2) = 30625+15005 = 45630
payoff probability 50 0.25 25 0.5 0 0.25 The table above provides a new gamble. Answer...