Suppose X and Y are {0, 1}-valued random variables with joint probability mass function given in the table below p(x, y) y 0 1 x 0 0.3 0.2 1 0.1 0.4 a. Determine E(Y |X = x) and var(Y |X = x). b. Use part a) to find E(Y ), and compare with the result using the marginal distribution of Y . c. Use part a) to find var(Y ), and compare with the result using the marginal distribution of Y .

0.2 kg/s of moist air at 45oC (DBT) and Humidity ratio 0.006 kgw/kgda (dry air) is mixed with 0.3 kg/s of moist air at 250C (DBT) and a humidity ratio of 0.018 kgw/kg da in an adiabatic mixing chamber. After mixing, the mixed air is heated to a final temperature of 40o C using a heater. Assume the barometric pressure to be 1 atm. Find

Enthalpies of both fluids

Temperature and humidity ratio of air after mixing.

Heat transfer rate in the heater.

The management of TTT Co must choose whether to go ahead with either of two mutually exclusive projects, A and B. The expected profits are as follows.

Required:

(a) Based on expected values, what would be the decision (project A or project B), if no information about demand were available.

(b) Calculate the value of perfect information about demand.

A pension fund manager is considering three assets. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill yielding 0.06. The probability distribution of the risky funds is as follows:

The correlation between the fund returns is 0.2.

What is the expected return of the optimal risky portfolio?

Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Suppose that the index model for stocks A and B is estimated from excess returns with the following results:

R_A =0.03 + 0.7R_M + e_A

R_B = -0.02 + 1.2R_M + e_B

σ_M = 0.2

R-square_A = 0.3;

R-square_B = 0.25

Assume you create for portfolio Q with investment proportions of 0.50 in P, 0.30 in the market index, and 0.20 in T-bills, portfolio P is composed of 60% Stock A and 40% Stock B. What is the standard deviation of the portfolio Q?

Group of answer choices

0.2556

0.2766

0.4800

0.1831

Using the following information, calculate the expected return and standard deviation of a portfolio with 50 percent in ABC and 50 percent in DEF. Then calculate the expected return and standard deviation of a portfolio where you invest 40 percent in ABC, 40 percent in DEF, and the rest in T-bills with a return of 3.5 percent.

Stocks A and B have the following returns in each of the states given below.

The probability of the good state is 0.5, the probability of the bad state is 0.3 and the probability of the ugly state is 0.2. What is the covariance between the returns of A and B? (Hint: The expected return of A is 10.5% and the expected return of B is 6%) What is the covariance between the return of A and the return of a risk-free asset which has an expected return of 5%?

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Use the following convention table for R-square.

Upload the ManBody data. Check which of the following four categories (BODYFAT, WEIGHT, HEIGHT, and KNEE) is the most correlated to AGE category. Make a scattered plot chart with X representing the most correlated category and Y representing the AGE, plot the line and compute the R-square. Answer the questions:

I) What category did you choose for X? (10 points)

• a. WEIGHT
• b. BODYFAT
• c. HEIGHT
• d. KNEE

II) Given the plot what is the estimated slope? (10 points)

• a. Between 0 and 0.1
• b. Between 0.1 and 0.3
• c. Between 0.3 and 1.3
• d. Between 1.3 and 10.5
• e. Between 10.5 and 40

III) What does each dot represent? (10 points)

• a. AGE
• b. WEIGHT
• c. HEIGHT
• d. PERSON
• e. BODY FAT

IV) On your chart, there should be a dot that is furthest on the right. What is its approximate X-coordinate? (10 points)

• a. Between 0 and 100
• b. Between 100 and 200
• c. Between 200 and 300
• d. Between 300 and 400

data set:https://www.limes.one/Content/DataFiles/Man_body.txt

Use the following convention table for R-square.

Upload the ManBody data. Check which of the following four categories (BODYFAT, WEIGHT, HEIGHT, and KNEE) is the most correlated to AGE category. Make a scattered plot chart with X representing the most correlated category and Y representing the AGE, plot the line and compute the R-square. Answer the questions:

I) What category did you choose for X? (10 points)

• a. WEIGHT
• b. BODYFAT
• c. HEIGHT
• d. KNEE

II) Given the plot what is the estimated slope? (10 points)

• a. Between 0 and 0.1
• b. Between 0.1 and 0.3
• c. Between 0.3 and 1.3
• d. Between 1.3 and 10.5
• e. Between 10.5 and 40

III) What does each dot represent? (10 points)

• a. AGE
• b. WEIGHT
• c. HEIGHT
• d. PERSON
• e. BODY FAT

IV) On your chart, there should be a dot that is furthest on the right. What is its approximate X-coordinate? (10 points)

• a. Between 0 and 100
• b. Between 100 and 200
• c. Between 200 and 300
• d. Between 300 and 400

data set:https://www.limes.one/Content/DataFiles/Man_body.txt