Consider a 2-year European put with a strike price of $52 on a stock whose current stock price is $50. Suppose that there are two time steps, and in each time step the stock price either moves up by 30% or moves down by 30%. Also suppose that risk-free rate is 7% per annum with continuous compounding. What is the value of the European put option?

Three cards are randomly selected from a deck of 52 cards. After every draw, the card is NOT replaced back in the deck. Find the probability of drawing a King, followed by two Aces in a row.

An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (e). What is the probability of passing the pop quiz if you guess the answers and you have to get 8 questions correct?

The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:

How many different ways can a 9-player baseball team be selected for an informal game if there are 25 available players? Which counting method do you use?

You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?

In a club there are 11 women and 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?

If a distribution follows the binomial distribution with n = 50 and probability of success of 0.25, calculate the mean and variance.

At a raffle, 1500 tickets are being sold for $2 each. There is one prize of $500, one prize of $250, one prize of $150, and one prize of $75. If you buy one ticket, what is the expected value of your gain?

Probability is:

Choose one • 10 points

The measure of how likely an event is to occur.

The ratio of total possible outcomes to desired outcomes.

Not conveyed as a decimal or a percent.

None of the above.

How many studs are needed to construct 100 feet of a 2 x 4 stud wall? The wall has one 8-footwide window, four 4-foot-wide windows, two 36-inch-wide doors, one 30-inch-wide door, four corners, two intersections, and eight hold downs located at corners. The stud spacing is 16 inches on center. Allow for two additional studs for each corner, intersection, or doorway; six additional studs for each window less than 6 feet in length; eight additional studs for each window 6 feet or more in width; and one additional stud for each hold down located at a corner

The local library if they get more patrons visiting by shifting some early morning hours to evening. They take a sample of days with morning hours included 8-5pm compared to 12-9pm.

8am-5pm hours: 50, 40, 60, 60, 70, 35, 40

12-9 PM hours : 40, 80, 70, 60, 85, 90, 70

1. Provide null and alternative hypotheses in formal terms and layperson's terms for the t test for independent samples

2. Do the math and reject or accept at a=.05

3. Explain the results in layperson's terms

4. Calculate and explain a 95% confidence interval in layperson's terms if appropriate.

The library thinks the average number of patrons for 12-9 PM hours is 60. Use the data for 12-9 from the previous question

1. Provide the null and alternative hypotheses formal and layperson’s informal terms for a t one-sample test.

2. Do the math and reject or accept at a=0.05

3. Explain the results in layperson’s terms

Water at 50 °F is being transported from one open reservoir to another open reservoir using a concrete pipe. The two reservoirs are 1.5 miles apart with a difference in surface elevations of 25 ft. Determine the minimum pipe diameter needed to carry 10 ft3 /s of water.

Tax Incidence: How do the effects of a tax differ between markets with different elasticities of supply? Consider two hypothetical markets. In both cases, the demand function is QD = 1000 - P The two supply functions are QS1 = P - 100 and QS2 = 2P - 650

a. Solve for equilibrium price and quantity for both cases and show that the equilibrium values are the same in these two cases (for QS1 and QD and for QS2 and QD). Plot the inverse supply and demand functions (with P on the vertical axis and Q on the horizontal axis) for the two markets on the same graph. (7)

b. Now suppose a tax is imposed in both markets, equal to $100 per unit purchased. Model this as a shift in the demand curve (so that QD now depends on P, the net price paid to the firm, plus the tax). Illustrate the new demand curve on your graph (label everything clearly). Derive the new equilibrium price (the net price received by the firm) and quantity for each of the two cases. In which case is the producer’s share of the tax burden greater? (7)

c. Calculate deadweight loss in each case. In which case is deadweight loss greater? (8)

oyota USA is studying the effect of regular versus high-octane gasoline on the fuel economy of its new high-performance, 3.5-liter, V6 engine. Ten executives are selected and asked to maintain records on the number of miles traveled per gallon of gas. The results are:

a. STATE THE NULL HYPOTHESIS AND ALTERNATE HYPOTHESIS

Assignment Description

This assignment focuses on programming basics; expressions, variables, constants, methods, selection and loops.

Danny runs an ice cream shop in the inner suburbs of Melbourne. Due to the growing number of customers, Danny has decided to take on extra casual employees. In order to manage payroll for his employees, Danny has decided to develop an employee payroll management system. Details of each employee to be maintained in the system will include; employee id, name, gender (M or F), phone number, hours worked, pay per hour, gross pay, net pay, and income tax payable.

The gross pay is calculated as the number of hours worked multiplied by pay per hour, while the net pay is calculated as the difference between gross pay and income tax payable of which income tax payable is calculated by multiplying gross pay by an income tax rate of 30%. Any hours over forty (40) is paid as an overtime hour at the rate of (2.5) times the base hourly rate.

For example, an employee who has worked a total of 45 hours with an hourly rate of $20 will have;

Regular pay=40*$20=$800

Overtime pay=5 * $20 * 2.5 = $250

Gross pay=$800 + $250 = $1,050

Income tax payable=$1050 * 30%=$315

Net pay=$1050-$315=$735

Task Requirements

Imagine you have been hired to develop this system. Familiarise yourself with the problem description and write a python program named payroll.py with the following functions:

1. Create a main () as a driver function in your payroll progam. Within the main (), you will declare all the required variables, and invoke the other methods described in the next step as required for calculations and displaying the program output.

2. Create additional functions in your payroll program for calculations as follows:
   1. Function to calculate the overtime hours
   2. Function to calculate the gross pay
   3. Function to calculate the income tax payable and
   4. Function to calculate the net pay

These functions needs to be invoked in correct order within your driver function main (), so that when your program executes, it should be able to produce an output as an employee’s pay slip like the example below.

Submission requirements:

1. Your assignment should include the following in the .ZIP archive:

• A Word report with sections containing:
  1. An overview of the problem description of the assignment
  2. Pseudocode as an algorithm for the program
  3. Screen shot/capture of the program output
  4. Statement of completion
  5. Acknowledgment of any help taken for assignment completion    
• Python file (payroll.py) that can be executed by your tutor

2. Instructions for archiving and submitting your files:

• Create a folder and name it with your student ID (MITnnnnnn, where nnnnnn are digits of your student number)
  • Copy your Word document and the python (payroll.py) files into that folder.
  • Zip the folder.
    1. Right-click on the folder
    2. In the pop-up menu select Send-to, Compressed (zipped)Folder
• Then submit this zipped folder in Moodle submission link

Marking criteria:

Program Demonstration: Students must demonstrate their program in week8 (lab time) to the tutor, and are expected to explain their implementation. Marks will be deducted (50% -maximum) for failing to do demonstration or poor explanation.

One mole of an ideal gas (C_P/R=7/2), is compressed in a steady-flow compressor from 2.5 bar and 25°C to 6.5 bar and 120°C. The compressor rejects 0.5 kJ as heat to the surrounding at 293K.

Calculate:

1.     The enthalpy change of the gas (in kJ)

2.     The entropy change of the gas (in J.mol^-1)

3.     The work required for the compression (in kJ)

4.     The ideal work of the process (in kJ)

5.     The thermodynamic efficiency

The lost work (in kJ)

"To Breakfast or Not to Breakfast?" by Richard Ayore

In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the

18^th, 20^th,   ,

birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come.

If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine.

Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, "This is why I always work more hours than you guys!"

And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in the table below, solve our problem. (Use

α = 0.05)

• State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

• Part (e)

  What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

• Part (f)

  What is the p-value?