16. What is the (approximate) probability that Die1+Die2+Die3=10? a. The probability is approximately 5%. b. The probability is approximately 10%. c. The probability is approximately 20%. d. The probability is approximately 25%. 17. What is the (approximate) probability that Die1+Die2+Die3>10? a. The probability is approximately 25%. b. The probability is approximately 35%. c. The probability is approximately 50%. d. The probability is approximately 75%. 18. What is the (approximate) probability that Die1+Die2>9? Careful: You need to create another column (and histogram) based on the first two dice or to argue directly by listing all possible outcomes! a. The probability is approximately 5%. b. The probability is approximately 15%. c. The probability is approximately 25%. d. The probability is approximately 35%.

Which of the following concepts is more reliable: theoretical probability, experimental probability, or simulations? Present your opinion and then give mathematical reasons or examples to support your opinion. Your post must have a minimum of 5 sentences.

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 12.80%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 18.87%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   4. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.

Select one:

In probability sampling, every item has a chance of being selected. There are 4 types of probability sampling. Can you name them and provide examples.

Bernoulli Trials. Probability is 0.26

Calculate the probability of 4 successes in 4 tries.

(Please show work)

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 8.20%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 25.07%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   4. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   
   
   

(1) Describe the difference between empirical and theoretical probability.
(2) Find the theoritical probability of tossing three coins and getting 2 heads, 1 tail.
(3) Toss three coins at once 50 times and record the out come of getting 2 heads, 1 tail.
(4)) Based on your observations, give the empirical probability of each result.

Consider the following probability distribution for stocks C and D:

If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation?

Select one:

a. 9.891%; 8.70%

b. 9.945%; 11.12%

c. 8.225%; 8.70%

d. 10.275%; 11.12%

Probability that a randomly selected student will weigh less than 140 lbs=0.2451

Probability that a randomly selected student will weigh more than 190 lbs=0.1292

Probability that a randomly selected student will weigh between 150 & 180 lbs= 0.4057

Using the information above, assume that you are going to randomly sample n=10 students.

1) What is the probability that the average of the selected student will be less than 140 lbs?

2) What is the probability that the average of the selected student will be more than 190 lbs?

3) What is the probability that the average of the selected student is between 150 & 180 lbs?

Suppose the return on portfolio P has the following probability distribution:

Type of market Probability Return

Bear 0.20 -20%

Normal 0.50 18%

Bull 0.30 50%

Assume that the risk free rate is 5% and the expected return and standard deviation on the market portfolio M is 0.15 and 0.20, respectively. The correlation coefficient between portfolio P and the market portfolio M is 0.80.

1. Is P efficient?

2. What is the beta of portfolio P?

3. What is the alpha of portfolio P? Is P overpriced or underpriced?