Machine Learning  Homework 1

CSE512 – Machine Learning 
Homework 1 Version 1 
This homework contains two questions. The last question requires programming. The maximum number
of points is 100 points. For this homework, you should review some material on probability. There are many
review notes and tutorials on the Internet and you are allowed to use Google to find them.
1 Question 1 – Probability (60 points)
Consider a positive integer N and let X1 and X2 be independent, discrete random variables uniformly
distributed from 1 to N. Let X = max(X1, X2) − X1. Compute:
1. (20 points) The expectation: E(X).
2. (20 points) The variance: V ar(X).
3. (20 points) The covariance: Cov(X, X1).
2 Question 2 – Programming (40 points)
Consider the random variables X1, X2, X defined as in Question 1. Write a Matlab (or equivalent Python)
function with the below signature: [E, V, C, H] = question2(N, M) The inputs to the above
function are positive integers N and M. M is the number of sample pairs of (X1, X2). The outputs of
the function are four scalars E, V, C, H for E(X), V ar(X), Cov(X, X1), and the entropy H(X). Plot
E, V, C, H as the function of M = 100, 200, 300, · · · , 9900, 10000 for N = 100. Produce four separate
plots for E, V, C, H. You are allowed to use built-in functions of Matlab such as mean, var, cov. Other
programming languages might have similar built-in functions, and you can use them if you want.
3 What to submit
You will need to submit both your code and your answers to questions on Blackboard. Put the answer file and
your code in a folder named: SUBID FirstName LastName (e.g., 10947XXXX lionel messi). Zip this folder
and submit the zip file on Blackboard. Yoursubmission must be a zip file, i.e, SUBID FirstName LastName.zip.
The answer file should be named: answers.pdf. The first page of the answers.pdf should be the filled cover
page at the end of this homework. The remaining of the answer file should contain:
1. Answers (and derivations) to Questions 1.1, 1.2, and 1.3
2. Four plots for E, V, C, H as the functions of M.
You can use Latex if you wish, but it is not compulsory.
4 Cheating warnings
Don’t cheat. You must do the homework yourself, otherwise you won’t learn. You cannot ask and discuss
with students from previous years. You cannot look up the solution online.
1
Cover page for answers.pdf
CSE512 Fall 2018 - Machine Learning - Homework 1
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