stems Engineering

MIDTERM EXAMINATION

Spring 2021

INSTRUCTIONS – READ INSTRUCTIONS

These instructions are not guidelines and must be followed. Failure to follow these instructions will result in a loss in marks:

· Submission Format: Begin the solution of each problem on a new page. The heading of each page should contain your name and the problem number. Please explain carefully your solution procedures and include sufficient working to follow your solution processes. Generally, an attempt must be made to be awarded partial credit when your answers are supported by your work; however, answers alone cannot be awarded partial credit.

· Submission Length: The maximum page length per problem is one page but you will not be penalized if you go into two pages. Solutions longer than two-pages will be penalized with a loss of marks. Conciseness of writing is an important presentation skill and you should make an effort to make your solution clear.

· Clarity: At least one mark from every question will be given for clarity.

· References and Assistance: You are allowed to use written reference material as long as all such material is properly referenced and acknowledged. You are not allowed to receive assistance from other individuals; the work that you submit for this examination is to be exclusively your own. When submitting this exam, you are asked to write and print your name (electronically sign) the following statement: "The work submitted for this exam is mine alone. I have not received assistance from, nor given assistance to, another individual."

· Examination Problems: If you believe a question statement is incomplete or ambiguous, you may make any reasonable assumptions required to complete or clarify the problem statement. Your assumptions must be stated clearly and, as long as they are not in conflict with the given problem statement or its logical context, will be considered as part of your problem solution.

PROBLEM ONE (5 Points)

Consider the following three projects:

YEAR	0	1	2	3	4	5	6
Project A	-$200	-$200	-$200	-$100	-$100	$0	$800
Project B	-$4,000	-$3,000	$0	$0	$0	$3,000	$6,000
Project C	-$5,000	$0	$0	$0	$0	$0	$7,000

Assume an interest rate of 5%, what project should be chosen? What about 10%?

What is the IRR for each project? What does it mean?

What other factors should you consider?

PROBLEM TWO (5 Points)

Choose a dataset. Use the techniques you learn in the course to do a statistical analysis on the dataset. Highlight some of the statistics that you have found and explain why they are meaningful.

I want to see a VERY clear report of your findings and what they mean in the real-world.

PROBLEM THREE (5 Points)

Data for this question can be found in the file entitled:

“Midterm Exam Data.csv”

The file contains 1000 data points, generated in an unknown way. You will be using this data to determine if there is any linear relationship within the sequence of the data.

Autocorrelation looks at the correlation that a data set has with itself. Let ‘Xi‘ represent the ‘i’ th data point.

1) Find the Pearson’s correlation coefficient between:

a) Xi and Xi+1

b) Xi and Xi+2

c) Xi and Xi+3

d) Xi and Xi+4

2) Why do we not need to bother working out the correlation between:

a) ‘Xi+1‘ and ‘Xi+4‘ ?

b) ‘Xi+2‘ and ‘Xi+2‘ ?

c) ‘Xi+2‘ and ‘Xi‘ ?

3) Create an ACF graph for the data and describe what the graph tells you.

PROBLEM FOUR (5 Points)

Three discrete random variables: X, Y. a is constant

Show, using the properties of expectation function only, that:

a) E(X+E(X)) – E(a(X-E(X)) = 2E(X)

b) var(X - aY) = var(X) + a2var(Y)

c) What assumption are we making about the variables?

PROBLEM FIVE (5 Points)

Consider the following gaming scenario. You have $3,000 in your pocket and have to choose between two options:

A) 70% chance of getting $100; otherwise you lose $50

B) 10% chance of getting $10; otherwise you get $50

What option should be taken?

1) Assuming you are risk neutral

2) Using Prospect Theory

Math and Comp Modeling in Systems Engineering

Use an alpha of 0.88 and a Kappa of 2.25

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PROBLEM SIX (5 Points)

What decision(s) should be taken in the following decision tree? And why? (Assuming that you are risk neutral) Show and explain your work.