Final Exam: Mathematics For Engineers (W2021)

MAT 8400 – Mathematics for Engineers (W2021)
MAT 8400
Mathematics for Engineers (W2021)
Final Exam
STUDENT NAME: Pukhraj Singh
This final exam covers material from Weeks 1 – 14.
NOTE: You must submit your midterm digitally on Brightspace → Activities → Assignments → Final Exam.
If you do not have a printer, you may complete your final exam on lined or blank paper. Make sure to write
clearly. Illegible work may result in a lower grade.
Each student is responsible for completing their own final exam. Cheating, including
plagiarism from online sources, and collaboration with peers, will not be tolerated. If
you have any questions about what constitutes plagiarism, consult Algonquin’s
Plagiarism Policy (AA20) and Policy on Academic Dishonesty and Discipline (AA18).
The final exam is out of a total of 70 points.
1
1. The M-file NumericalMethod.m was submitted by a previous

student from MAT 8400. You have been assigned the following two
tasks: (1) determining the type of numerical method in the code,
and (2) debugging the code.
(5 points each)
In your own words, answer the following questions:

a) What is the purpose of this M-file? In other words, what
numerical method has been coded in this file? Justify your
answer by citing specific lines of code.
b) Does the M-file work as intended? If not, why not? Which line(s)
of code are incorrect?
c) What do you suggest should be done to fix and/or improve the
M-file?
Figure 1: Source code for NumericalMethod.m.

Ans :- The following code contains Reimann Sum Right area calculating code. It
is used to calculate area inside the curve by drawing infinitesimal small
rectangles which are going to be splitted into equal intervals and we take all the
right hand points of that interval points to calculate the area of the curve.
Error:- no n value in the function specified ;
2
No n value for the for loop defined which should be 50 according to division in
the code.
There should be an increment line inside the for loop where x=x+dx.
Also there should be b-a, not a-b
Also see rest on the pdf file bring submitted.
3
2. A set of experiments was conducted to assess automated QA/QC

procedures at a wafer fabrication facility. The following dataset
was collected:
Table 1: Automated QA/QC Assessments at Wafer Fab Facility1

Experiment Wafer
Thickness of Wafer (µm)
# Rejected?
1 774.9 No
2 775.0 No
3 774.7 No
4 774.8 Yes
5 775.1 No
6 775.0 No
7 775.2 No
8 774.7 Yes
9 775.3 Yes
10 775.2 No
1: According to manufacturers specification, a wafer thickness of >775.2 µm is considered too
thick and thickness of <774.8 µm is considered too thin.
Let’s define event A as a wafer having a thickness that is out of

specifications.
Let’s define event B as a wafer being rejected.
Determine the following (5 points each):
a) P ( A  B ) = 4/10 = 2/5
b) Are events A and B independent? Why or why not? No,
c) P ( B | A) = 2/3
4
3. Answer the following questions in your own words. Do not copy

content from the lecture notes or other resources. Each question is
worth 5 points.
a. Describe the purpose and usefulness of Monte Carlo
simulations.
b. Discuss the similarities and differences between ‘mean’,
‘median’, and ‘mode’.
c. Explain the term confidence interval on the mean. Why is a
100% confidence interval never used in statistics?
d. Choose a probability distribution covered in this course.
Discuss its purpose, define its parameters, and discuss their
significance.
e. Explain the similarities and differences between interpolation
and extrapolation.
5
4. Consider the following dataset:
Table 2: Operative Time for Robot-Assisted Roux-en-Y Gastric Bypass

(RA-RYGB) (in min)
127.90 132.39 157.56 144.18 134.63 117.91 139.65 154.98
136.84 143.96 137.75 107.91 114.89 132.13 130.90 156.31
139.10 144.85 149.94 147.06 149.95 138.81 139.66 141.11
143.18 119.97 141.44 147.17 135.36 139.91 128.51 122.75
132.79 123.41 137.98 134.72 115.88 150.31 131.03 152.34
132.55 162.84 145.35 119.95 156.35 135.37 132.25 115.09
133.15 151.67 139.77 139.18 151.93 117.89 130.73 128.34
122.00 146.28 140.74 134.06 128.16 147.32 137.64 127.22
139.47 149.09 155.82 145.21 141.11 133.04 137.24 125.12
157.27 118.40 133.80 136.25 145.06 108.39 141.83 149.01
126.68 156.19 142.23 159.30 158.04 137.95 110.96 144.87
140.06 141.48 142.72 146.43 155.14 119.42 125.74 131.01
147.30 158.15 132.10 140.62 136.14 110.12 136.21 154.54
a) Use MATLAB to fit the data with a probability distribution taught

during the lectures. Report the [h,p] values. Justify your choice
of probability distribution. Report the important distribution
parameters (7 points).
Ans- I choose Weibull because this distribution is continuous
type and not discrete so Weibull will be the best to solve for
continuous type dataset.
b) Give 90%, 95%, and 99% confidence intervals on the important
distribution parameters (8 points).
6
7
95 percent is set by default so =
90 percent
99 percent

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MAT 8400 – Mathematics for Engineers (W2021)

STUDENT NAME: Pukhraj Singh

This final exam covers material from Weeks 1 – 14.

The final exam is out of a total of 70 points.

1. The M-file NumericalMethod.m was submitted by a previous

In your own words, answer the following questions:

Figure 1: Source code for NumericalMethod.m.

2. A set of experiments was conducted to assess automated QA/QC

Table 1: Automated QA/QC Assessments at Wafer Fab Facility1

Let’s define event A as a wafer having a thickness that is out of

Determine the following (5 points each):

3. Answer the following questions in your own words. Do not copy

4. Consider the following dataset:

Table 2: Operative Time for Robot-Assisted Roux-en-Y Gastric Bypass

a) Use MATLAB to fit the data with a probability distribution taught

95 percent is set by default so =

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