EECE5644 Summer 1 2022 – Assignment 1
Submit: Tuesday, 2022-May-31 before 11:59 EDT (upload PDF to Canvas)
Please submit your solutions at the classroom assignments page in Canvas. Please upload a
single PDF file that includes all math, numerical and visual results, and code (as an appendix or as
a link to your online code repository for this assignment). If you point to an online repository, do
NOT edit the contents after the deadline, because TAs may interpret a last-modified timestamp past
the deadline as a late submission of the assignment. Only the contents of the PDF will be graded.
Please do NOT link from the PDF to external documents online where results may be presented
(e.g. online Notebooks of any kind).
This is a graded assignment, and the entirety of your submission must contain only your own
work. You may benefit from publicly available literature including software (not from classmates),
as long as these sources are properly acknowledged in your submission. Copying math or code
from each other is not allowed and will be considered as academic dishonesty. While there cannot
be any written material exchange between classmates, verbal discussions to help each other are
acceptable. Discussing with the instructor, the teaching assistant, and classmates at open office
periods to get clarification or to eliminate doubts are acceptable.
By submitting a PDF file in response to this take-home assignment, you are declaring that the
contents of your submission, and the associated code is your own work, except as noted in your
citations of external resources.
1
Question 1 (30%)
The probability density function (pdf) for a 3-dimensional real-valued random vector X is as
follows: p(x) = p(x|L = 0)P(L = 0)+ p(x|L = 1)P(L = 1). Here L is the true class label that
indicates which class-label-conditioned pdf generates the data.
The class priors are P(L = 0) = 0.65 and P(L = 1) = 0.35. The class class-conditional pdfs are
p(x|L = 0) = g(x|m0,C0) and p(x|L = 1) = g(x|m1,C1), where g(x|m,C) is a multivariate Gaus-
sian probability density function with mean vector m and covariance matrix C. The parameters of
the class-conditional Gaussian pdfs are:
m0 =
1/2 1/2
1/2
C0 =
1 0.5 0.3 0.5 1 0.5
0.3 0.5 1
m1 =
11
1
C1 =
1 0.3 0.20.3 1 0.3
0.2 0.3 1
