Question 1: You have to choose a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $ 150, and behind the other is a round-the-world trip worth $7200. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection?
Do not use comma separator in your answer.
Round your answer to two decimal places.
Question 2: You are considering investing in a stock, and is aware that the return on that investment is particularly sensitive to how the economy is performing. Your analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return on the investment.
|
State
|
Probability
|
Return
|
|
Boom
|
0.1
|
25.00%
|
|
Good
|
0.4
|
15.00%
|
|
Level
|
0.3
|
10.00%
|
|
Slump
|
0.2
|
-5.00%
|
Do not use comma separator in your answer.
Round your answer to four decimal places.
Question 3: You are considering investing in a stock, and is aware that the return on that investment is particularly sensitive to how the economy is performing. Your analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the standard deviation of the return on the investment.
|
State
|
Probability
|
Return
|
|
Boom
|
0.1
|
25.00%
|
|
Good
|
0.4
|
15.00%
|
|
Level
|
0.3
|
10.00%
|
|
Slump
|
0.2
|
-5.00%
|
Do not use comma separator in your answer.
Round your answer to four decimal places.
Question 4: Given the returns and probabilities for the three possible states listed below, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively.
|
Outcome
|
Probability
|
Return(A)
|
Return(B)
|
|
Good
|
0.35
|
0.3
|
0.5
|
|
OK
|
0.5
|
0.1
|
0.1
|
|
Poor
|
0.15
|
-0.25
|
-0.3
|
Do not use comma separator in your answer.
Round your answer to four decimal places.
Question 5: You know that the average college student eats 0.75 pounds of food at lunch. If the standard deviation of that eating is 0.2 pounds of food, then what is the total amount of food that a cafeteria should have on hand to be 95 percent confident that it will not run out of food when feeding 50 college students? (Look in the text for properties of returns that follow a normal distribution.)
|
17.90 pounds
|
|
21.05 pounds
|
|
53.95 pounds
|
|
57.10 pounds
|
Question 6: There are three securities in the market. The following chart shows their possible payoffs.
|
State
|
Probability of Outcome
|
Return on Security 1
|
Return on Security 2
|
Return on Security 3
|
|
1
|
.15
|
.25
|
.25
|
.10
|
|
2
|
.15
|
.2
|
.15
|
.15
|
|
3
|
.35
|
.15
|
.20
|
.20
|
|
4
|
.15
|
.10
|
.10
|
.25
|
What is the expected return of a portfolio with half of its funds invested in Security 1 and the other half in Security 2? NOTE:(The probabilities do not add up to one as they should. Calculate this as if they did!)
Do not use comma separator for thousands in your answer.
Round your answer to four decimal places.
Question 7: You have to choose a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $ 150, and behind the other is a round-the-world trip worth $7200. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the standard deviation of that selection?
Do not use comma separator in your answer.
Round your answer to two decimal places.