A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided. Use the​ chi-squaregoodness-of-fit test to​ decide, at a significance​ level of 0.10, whether the distribution of the variable differs from the given distribution. (You need to add the expected column based on the distribution)

a.       Specify which Chi-Square test you are doing (Goodness-of-Fit or Test for Independence):

b.       Formulate the null (H0) and alternate (HA) hypotheses:

c.       Specify the level of significance (alpha, a):

d.       What is the value of the test statistic?

e.       What is the critical value?

f.        Do you reject H0 or fail to reject H0?

g.       To validate your results, we’ll also check our p-value. What is the p-value?

h.       Based on your p-value, do you reject or do not reject?

i.         State your summary statement of the conclusion in non-technical terms.

Suppose that in this particular economy, there are four assets. Assets 1, 2, and 3 are risky and the fourth asset is risk-free.

The correlations of returns are described in the following table:

And the standard deviation of the return of each stock is:

Finally, the number of shares and price of each stock is:

1. Construct the variance-covariance matrix for the returns of the three risky assets.

2. Compute the weights of the market portfolio. That is, show that the weight of stock 1 in the market portfolio is 1/6, the weight of stock 2 is 3/6 and the weight of stock 3 is 2/6.

3. If CAPM assumptions hold, compute the investor’s optimal risky portfolio.

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

a. Find the expected value of the cash flow for each apartment complex. (Enter the answers in thousands.)

b. What is the coefficient of variation for each apartment complex? (Do not round intermediate calculations. Round the final answers to 4 decimal places.)

c. Which apartment complex has more risk?

• Hillcrest Apartments

• Windy Acres

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

a. Find the expected value of the cash flow for each apartment complex. (Enter the answers in thousands.)

b. What is the coefficient of variation for each apartment complex? (Do not round intermediate calculations. Round the final answers to 4 decimal places.)

c. Which apartment complex has more risk?

• Windy Acres

• Hillcrest Apartments

n insurance portfolio consists of two homogeneous groups of clients; N i, (i = 1 , 2) denotes the number of claims occurred in the ith group in a fixed time period. Assume that the r.v.'s N 1, N 2 are independent and have Poisson distributions, with expected values 200 and 300, respectively.

The amount of an individual claim in the first group is a r.v. equal to either 10 or 20 with respective probabilities 0.3 and 0.7, while the amount of an individual claim in the second group equals 20 or 30 with respective probabilities 0.1 and 0.9.

Let N be the total number of claims, and let S be the total aggregate claim.

Find E { S } and V a r { S }.

(Hint: Compute E { Y i } and E { Y i 2 } proceeding from the result of Question 10 and use Propositions 1-2 that we proved in class regarding E { S } and V a r { S } in the case where N is a Poisson r.v.)

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

a. Find the expected value of the cash flow for each apartment complex. (Enter the answers in thousands.)

b. What is the coefficient of variation for each apartment complex? (Do not round intermediate calculations. Round the final answers to 4 decimal places.)

c. Which apartment complex has more risk?

• Windy Acres

• Hillcrest Apartments

The table below shows primary school enrollment for a certain country. Here, xx represents the number of years after 18201820, and yy represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x   y
0   0.1
5   0.1
10   0.1
15   0.2
20   0.2
25   0.3
30   0.4
35   0.5
40   0.6
45   1.1
50   1.5
55   3.0
60   4.5
65   5.5
70   6.1
75   6.8
80   7.0
85   8.0
90   9.3
95   10.7
100   12.4
105   14.1
110   16.6
115   17.5
120   19.7
125   19.4
130   32.7
135   40.9
140   47.6
145   57.8
150   57.0
155   61.7
160   63.2
165   75.0
170   76.5
175   96.0
180   92.0
185   100.0
190   100.0

Provide your answer below:

y =  x -

A daily commuter crosses two traffic signals on his way to work. The probability that he will be stopped at the first signal is 0.47, at the second signal is 0.30, and the probability that he may not have to stop at any of the two signals is 0.3. Answer all the questions to 2 decimal places where appropriate.

1. What is the probability that the commuter will be stopped at both signals?

2. What is the probability that he will be stopped at the second, but not at the first signal?

3. What is the probability that he will be stopped at exactly one signal given that he was not stopped at the first signal?

4. "Stopping at signal 1 is independent of stopping at signal 2." This statement is:
a.Incorrect True because P(stopping at both signals) = P(stopping at signal 1)×P(stopping at signal )
b.ncorrect False because P(stopping at both signals) ≠ 0
c.Incorrect True because P(stopping at both signals) ≠ 0
d.Correct: False because P(stopping at both signals) ≠ P(stopping at signal 1)×P(stopping at signal 2)

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.

A sample of 57 stocks traded on the NYSE that day showed that 28 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α=0.10α=0.10.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =___________

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ___________

Please show me step by step how you got the P-vaule!!!!!!

HAND CALCULATIONS ONLY. NO EXCEL.

You forecast there are three potential scenarios for the economy: a bull, flat, and bear market. You also estimate the returns for a stock and bond mutual fund as follows:

Using this information, you find for the stock fund: E(r_S)=0.032 and σ_S=0.1469, and for the bond fund: E(r_B)=0.016 and σ_B=0.0561.

1. Compute the covariance between the stock and bond fund. (Record your answer to at least four decimal places) (10 points)

2. Compute the correlation coefficient between the stock and bond fund. (Record your answer to at least four decimal places) (10 points)

You put 70% of your portfolio in the stock fund and the remaining 30% in the bond fund.

3. Compute the standard deviation of your portfolio. (Record your answer to at least four decimal places) (10 points)