1. Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and pay-offs are given below:

Outcome	Probability	Pay-offs
A	.3	$100
B	?	50
C	.2	?

The expected value of the investment is $25. Although all the information is correct, information is missing.

a. What is the probability of outcome B?

b. What is the pay-off of outcome C?

c. What is the variance of the investment?

d. What is the standard deviation of the investment?

2. The relationship between income and total utility for three investors (A, B, and C) is shown in the tables below.

A B C

Income TU Income TU Income TU

5,000 14 5,000 4 5,000 6

10,000 24 10,000 8 10,000 14

15,000 32 15,000 12 15,000 24

20,000 38 20,000 16 20,000 36

25,000 43 25,000 20 25,000 52

30,000 47 30,000 24 30,000 72

35,000 49 35,000 28 35,000 100

Each investor has been confronted with the following three investment opportunities. The first opportunity is an investment which pays $15,000 risk free. Opportunity two offers a 0.4 probability of a $25,000 payment and a 0.6 probability of paying $10,000. The final investment will either pay $35,000 with a probability of 0.25 or $5,000 with a probability of 0.75. Determine the alternative each of the above investors would choose. What could be risk attitude of these investors (marginal utility can help)?