1. Consider the following production function for bus transportation in a particular city:

Q= aL^B1F^B2K^B3

Where Fuel input in gallons = F

Capital input in number of busses = K

Labor input in worker hours = L

Output in millions of bus miles = Q

We estimate the various parameters as follows using historical data:

                                    α=0.0012, β1=0.45, β2=0.2, β3=0.3

a) Determine output elasticities for Labor.

b) Suppose that labor hours increase by 10%. By what percentage will output increase?

Income

A. The mean or average of the ranked above data for a village in Peru is:

a. $245.44

b. $345.44

c. $123.44

d. $200.56

B. Suppose that the covariance between the ranked income and the cumulative distribution of income is 33.24. The Gini coefficient for this village is approximately:

a. .212
b. .223

c. .271

d. .281

A study to determine haemoglobin due to the strength of medication categorised into 5 groups were conducted on 27 women aged 18-40 years. The table below displays the data and the relevant descriptive quantities.

Medication strength
A B C D E
0.8 0.7 1.2 1.0 0.6
0.6 0.8 1.0 0.9 0.4
0.6 0.5 0.9 0.9 0.4
0.5 0.5 1.2 1.1 0.7

0.6 1.3 0.7 0.3

0.9 0.8
0.7   

a) Normality assumption was checked, and it was not normally distributed. Hence, determine if the five groups of medication strength have the same median haemoglobin level? 

b) Write a brief summary of what the result show.  

1. A randomly selected freshman takes English with probability 0.7, takes Math with probability 0.5, and takes either English or Math with probability 0.8. What is the probability of taking both English and Math?

2. Two mutually exclusive events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

3. Two independent events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

4. If P (A | B) = 0.8 and P(B) = 0.6, find P (A and B).

5. Given the following table, evaluate

P(No), P (Woman and Yes), P (Man | Yes), P (No opinion | Woman), P(Men or No Opinion).

Are Women and No mutually exclusive?

Are Women and No independent?

6. A box contains 5 blue chips, 4 red chips, and 7 green chips. Select 10 chips at random.

1. In how many ways can this be done?
2. How many of these selections consist of 3 blue chips, 2 red chips, and 5 green chips?

(do not simplify your answers, leave them in terms of binomial coefficients).

MATLAB CODE: Making cubic spline iterpolation function. Then, To solve use Tridiagonal matrix algorithm(TDMA)

Suppose we have 3 assets: Expected returns = [0.1 0.15 0.12] Standard déviations = [0.2 0.25 0.18] Correlations = [1 0.8 0.4 0.8 1 0.3 0.4 0.3 1] Find all possible pairwise two-asset portfolios and plot on a backround of random portfolios of all three assets. Comment on the efficient frontier.

A study to determine haemoglobin due to the strength of medication categorised into 5 groups were conducted on 27 women aged 18-40 years. The table below displays the data and the relevant descriptive quantities. Medication strength A B C D E 0.8 0.7 1.2 1.0 0.6 0.6 0.8 1.0 0.9 0.4 0.6 0.5 0.9 0.9 0.4 0.5 0.5 1.2 1.1 0.7 0.6 1.3 0.7 0.3 0.9 0.8 0.7 a) Normality assumption was checked, and it was not normally distributed. Hence, determine if the five groups of medication strength have the same median haemoglobin level? [5 marks] b) Write a brief summary of what the result show. [2 marks]

1. An experiment consists of four outcomes (A, B, C, D) with P(A) = 0.2, P(B) = 0.3, and P(C) = 0.4.  The P(D) is

1. 0.500
2. 0.024
3. 0.100
4. 0.900

2. Given that event E has a probability of 0.3, the probability of the complement of

event E

1. cannot be determined with the above information
2. can have any value between zero and one
3. must be 0.7
4. is 0.3

3. If P(A) = 0.38, P(B) = 0.83, and P(A Ç B) = 0.57; then P(A È B) =  

1. 1.21
2. 0.64
3. 0.78
4. 1.78

4. If P(A) = 0.62, P(B) = 0.47, and P(A È B) = 0.88; then P(A Ç B) =  

1. 0.2914
2. 1.9700
3. 0.2700
4. 0.2100

5. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then

P(A Ç B)=

1. 0.30
2. 0.15
3. 0.00
4. 0.20

6. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then

P(A È B)=

1. 0.00
2. 0.15
3. 0.8
4. 0.7

7. If P(A) = 0.80, P(B) = 0.65, and P(A Ç B)= 0.38, then P(B\A) =

1. 0.650
2. 0.585
3. 0.475
4. not enough information is given to answer this question

8. If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A\B) =

1. 0.209
2. 0.00
3. 0.55

      d.   0.38

9.  The measure of location that is the most likely to be influenced by extreme values in

      the data set is

1. the range
2. the median
3. the mode
4. the mean

10.  The median is

      a.  the 50th percentile

      b.  another name for the variance

      c.  the difference between the largest and smallest values

      d.  the difference between the third quartile and the first quartile

11.  Which measure of location is meaningful when the data are qualitative?

       a.  the mean

       b.  the midrange

       c.  the median       

       d.  the mode

12.  The sum of deviations of the individual data elements from their mean is

      a.  always greater than zero

      b.  always less than zero

      c.  sometimes greater than and sometimes less than zero, depending on the data

          elements

      d.  always equal to zero

13.  The standard deviation of a sample of 49 observations equals 6.  The variance of the

       sample equals

      a. 6

      b. 7

      c. 36

      d. 625

    14.  Which of the following is a measure of location?  

1. Range
2. s
3. s²
4. µ

15.  Which of the following is NOT a measure of location?  

1. Range
2. Mean
3. Median
4. Mode
5. All of the above are measures of location

16.  A method of assigning probabilities based upon best educated guess is referred to as  

a)    relative frequency method

b)    probability method

c)    classical method

d)    subjective method

17.  Find the sample standard deviation and variance of the values: 12, 14, 28, 33, and 19.   

      Units for data values in miles. Show all work with correct notation, decimal places  

       and units.

Which has a higher systematic risk and why?

(A) a stock with a slope(beta) of 0.8 and R^2 of 0.7

(B) a stock with a slope(beta) of 0.4 and R^2 of 0.3

You suspect that townsfolk near Gloomsville are getting cancer because of a new toxic waste dump built in town. So, suspecting this is in the water, you look at cancer rates up to 20 miles downstream from the dump site. Is cancer evenly distributed along those 20 miles? The data to answer this question are in the table above.

I will have to solve this using Excel. Specifically what should I do? What functions could I use? For the question, I have to

1. A null and alternative hypothesis stated, as appropriate and for each hypothesis tested. may involve several hypothesis tests.

2. Choose the most appropriate test. Explain how you have met the assumptions of the test or why the test is robust to violations of the assumptions.

3. State explicitly what test(s) you are using.

4. If you fail to reject the null hypothesis, calculate the power of the test.