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

1. Calculate the expected rate of return,  , for Stock B ( = 6.70%.) 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 = 26.90%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

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

   Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.

   Stock A:  

   Stock B:  

a. Based on the table above, construct an equal-weighted (50/50) portfolio of Investments B and C. What is the expected rate of return and standard deviation of the portfolio?

b. Now construct an equal-weighted (50/50) portfolio of Investments B and D. What is the expected rate of return and standard deviation of the portfolio?

Part A:

   E(R) for BC portfolio: Note: format answer is 12.3%

   SD for BC portfolio: Note: format answer is 1.2%

Part B:

   E(R) for BD portfolio: Note: format answer is 12.3%

   SD for BD portfolio: Note: format answer is 1.2%

The random variable X can take on the values 1, 2 and 3 and the random variable Y can take on the values 1, 3, and 4. The joint probability distribution of X and Y is given in the following table:

a. What value should go in the blank cell?

b. Describe in words and notation the event that has probability 0.2 in the table.

c. Calculate the marginal distribution of X and the marginal distribution of Y.

d. Are X and Y independent events? Show why or why not with calculations.

e. Calculate the conditional distribution of X given Y=1.

f. Calculate E(X) and E(Y).

g. Calculate V(X) and V(Y).

h. Calculate E(X|Y=1).

An outbreak of Salmonella-related illness was attributed to ice cream produced at a certain factory. Scientists are interested to know whether the mean level of Salmonella in the ice cream is greater than 0.2 MPN/g. A random sample of 20 batches of ice cream was selected and the level of Salmonella measured. The levels (in MPN/g) were:

0.593, 0.142, 0.329, 0.691, 0.231, 0.793, 0.519, 0.392, 0.418, 0.219 0.684, 0.253, 0.439, 0.782, 0.333, 0.894, 0.623, 0.445, 0.521, 0.544

a)Read the data in R using a vector. Show your codes only but not the output.

b)State the two hypotheses of interest.

c) Is there evidence that the mean level of Salmonella in the icecream is greater than 0.2 MPN/g? Assume a Normal distribution and use α =0.05. Show your codes and result/output from R.

d) Interpret your finding in c)

Q1/Given the following information about the returns of stocks A, B, and C, what is the expected return of a portfolio invested 30% in stock A, 40% in stock B, and 30% in stock C?

Enter answer in percents.

Q2/A stock has an expected return of 10.2 percent, the risk-free rate is 5.7 percent, and the market risk premium is 6.5 percent. What must the beta of this stock be?

Q3/You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 0.76 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?

A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20% of the complaints should have been filed on Monday. She randomly selected 50 complaints and checked the day that they were submitted. In those complaints 13 were submitted on a Monday.

The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints submitted on a Monday is different from 20%.

(a) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test.

(b) Use Excel to test whether the true proportion of complaints submitted on a Monday is different from 20%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

• A sample of size 10 is taken from the first population: Sample mean of 101.2 and sample variance of 18.1
• A sample of size 14 is taken from the second population: Sample mean of 98.7 and sample variance of 9.7

1)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the rejection region.

2)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the observed value of the test statistic.

3)If a significance level, not necessarily equal to the choice of questions 1 and 2, is used when the decision on pooling is made and pooling is found to be not appropriate: We wish to compare the means of two populations at α = 0.1 level, testing: Ho: μ1 = μ2 (against H1: μ1 ≠ μ2). Find an interval for the P-value.

Need an answer for 3).

• A sample of size 10 is taken from the first population: Sample mean of 101.2 and sample variance of 18.1
• A sample of size 14 is taken from the second population: Sample mean of 98.7 and sample variance of 9.7

1)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the rejection region.

2)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the observed value of the test statistic.

3)If a significance level, not necessarily equal to the choice of questions 1 and 2, is used when the decision on pooling is made and pooling is found to be not appropriate: We wish to compare the means of two populations at α = 0.1 level, testing: Ho: μ1 = μ2 (against H1: μ1 > μ2). Find the rejection region.

answer for 3) is important

• A sample of size 10 is taken from the first population: Sample mean of 101.2 and sample variance of 18.1
• A sample of size 14 is taken from the second population: Sample mean of 98.7 and sample variance of 9.7

1)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the rejection region.

2)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the observed value of the test statistic.

3)If a significance level, not necessarily equal to the choice of questions 1 and 2, is used when the decision on pooling is made and pooling is found to be appropriate: We wish to compare the means of two populations at α = 0.1 level, testing: Ho: μ1 = μ2 (against H1: μ1 ≠ μ2). Find the rejection region.

Need an answer for 3).