The following system is a small power generating plant which contains a boiler, a superheater, a turbine and a condenser. Describe each part of the system with reference to the equations required in terms of heat transfer and work transfer. The feed water flows at 1 tonne/hr at 50°C. The output pressure is 6 bar with a dryness fraction is 0.9 and the efficiency of the boiler is 75%. The calorific value of the fuel is 38MJ/kg. Determine the fuel flow rate.

The superheater adds 300°C of super heat, determine the energy input to the superheater assuming no heat loss.

The turbine is 70% efficient and the output steam is at 0.2 bar and 0.8 dryness fraction. Determine the output power of the turbine.

Which stock, A or B, or both of them, is preferable to add to the diversified portfolio, and why? if the information about each stock as follows:

stock A: Average annual return-117.4, Average return 11.7%, Standard deviation 8.9, Coefficient of variation 0.8, Required return 11.8, beta 1.6

stock B: Average annual return-111.4, Average return 11.1%, Standard deviation 2.7, Coefficient of variation 0.2, Required return 10.3, beta 1.1

Risk free rate 7%

Market return 10%

Covariance 11.95

Correlation coefficient 0.48

Return on a portfolio (with both stocks A and B) 11.44

Standard deviation of a portfolio 5.26

Q5. You are a theater owner fortunate to book a summer box office hit into your single theater. You are now planning the length of its run. Your share of the film’s projected box office is

R = 10 W -0.25 (W)^2, where R is in thousands of dollars and W is the number of weeks that the movie runs. The average operating cost of your theater is AC =MC = $5 thousand per week.

1. To maximize your profit, how many weeks should the movie run? What is your profit?

You realize that your typical movie makes an average operating profit of $1.5 thousand per week. How does this fact affect your decision in part a above if at all?

On November 14, Thorogood Enterprises announced that the public and acrimonious battle with its current CEO had been resolved. Under the terms of the deal, the CEO would step down from his position immediately. In exchange, he was given a generous severance package. Given the information below, calculate the cumulative abnormal return (CAR) around this announcement. Date Market Return (%) Company Return (%) Nov 7 1.7 1.3 Nov 8 1.5 1.3 Nov 9 -1.4 -0.2 Nov 10 −0.6 −0.5 Nov 11 2.5 1.0 Nov 14 −1.3 3.0 Nov 15 0.1 0.1 Nov 16 0.9 1.9 Nov 17 1.4 0.8 Nov 18 −1.4 0.0 Nov 21 1.5 0.2 Assume the company has an expected return equal to the market return. (A negative value should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. ) What is the percentage cumulative abnormal return (CAR) on Day "-2", which is relative to the announcement date of the event?

Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in an eyeglass and the probability that it will take that number of days are in the table. Table #5.1.8: Number of Days to Fix DefectsNumber of daysProbabilities

1 24.9%

2 10.8%

3 9.1%

4 12.3%

5 13.3%

6 11.4%

7 7.0%

8 4.6%

9 1.9%

10 1.3%

11 1.0%

12 0.8%

13 0.6%

14 0.4%

15 0.2%

16 0.2%

17 0.1%

18 0.1%

State the random variable.

b.)Draw a histogram of the number of days to fix defects

c.)Find the mean number of days to fix defects.

d.)Find the variance for the number of days to fix defects

. e.)Find the standard deviation for the number of days to fix defects.

f.)Find probability that a lens will take at least 16 days to make a fix the defect.

g.)Is it unusual for a lens to take 16 days to fix a defect?

h.)If it does take 16 days for eyeglasses to be repaired, what would you think?

The Longmont company in Charlette, North Carolina, asked you to develop quarterly forecasts of combine sales for next year. Combine sales are seasonal, and the data on the quarterly sales for the last four years are as follows:

Chad Johnson estimates the total demand for the next year (Year 5) at Longmont. Use the seasonally adjusted exponential smoothing model to develop the forecast for each quarter. Use the appropriate assumptions to intialize the model. Required column headings in Excel are Periods, Years, Quarters, Demand (sales data), Base Value, Seasonality Index, Trend, and Forecast. Use 3 decimal places. Set up your solution using α = 0.2, β= 0.2, γ = 0.8, MAD = 54.845, and Bias = 4.926.

The table will consist of 8 colums and 20 rows for the 20 periods.

Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.

(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.)
$  to $  

(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.)
$  to $  

(c) Do the intervals in parts (a) and (b) contain the value (μ₁ − μ₂) = 0?

Yes, the interval in part (a) contains (μ₁ − μ₂) = 0.Yes, the interval in part (b) contains (μ₁ − μ₂) = 0.    Yes, both intervals contain (μ₁ − μ₂) = 0.No, neither interval contains (μ₁ − μ₂) = 0.

Why is this of interest to the researcher?

If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there is no difference in the average room rates for the two hotels.    If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.

(d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel C chains.    

Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.   

a.

b.

Assume the online test in HA1011 has 15 multiple questions. Each question has five possible answers, of which only one is correct.

1. What is the probability that guesswork will yield at least seven correct answers?

2. What is the expected number of correct answers by guesswork?

At Delta limited the Chief Administrative Manager analyzed the number of incoming faxes. After an analysis, the manager determined the probability distribution of the number of pages per fax as follows:

Required:
Compute the mean and the variance of the number of pages per fax.

Consider the following scenario analysis:

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a.What is rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

Recession rate of return:?%

Normal Economy rate of return:?%

Boom rate of return:?%

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Expected rate of return:?%

Standart deviation:?%

Let U be a Standard Uniform random variable. Show all the steps required to generate:

1. a Binomial random variable with parameters n = 12 and p = 0.6
2. a discrete random variable with the distribution P(x), where P(0) = 0.4, P(3) = 0.1, P(7) = 0.2, P(14) = 0.3;
3. a continuous random variable with the density f(x) = 4x 3 , 0 < x < 1;
4. a continuous random variable with the density f(x) = (1/18)x 2 , -3 < x < 3;
5. a continuous random variable with the density f(x) = (5/128)x 1/4 , 0 < x < 16