CS 6375 Homework 0 Due: 01/21/2015, 2:30pm. Total: 100 points. 1. [15 pts] Describe an application that you think machine learning approaches are appropriate (maybe machine learning is already used or you think that can be used). Explain the task clearly and how machine learning is or can be used. Please try to find an application that is not discussed in the textbook or our class. 2. [10 pts] Assume you are going to build a system to detect spam emails, that is, your task is to determine whether an email is legitimate or spam. What kind of attributes/features would you use for this task? 3. [75 pts] The following problems are meant to help you refresh your memory on some concepts related to math and statistics, which we will need in this course. 3.1. Probability and statistics a) [5 pts] What is the probability of getting exactly 8 heads when flipping a fair coin 10 times? b) [5 pts] For a fair coin, when you toss it 10 times, which of the following sequence is more likely to occur? HHHHHHHHHH or HTHTHHTTHT c) [5 pts] If you don’t know whether a coin is fair or biased (towards head or tail), when you see the sequences above from another person’s tossing, what can say about whether the coin is likely to be fair or biased? d) [5 pts] Assume P(A)=0.4 and P(B)=0.25, what is the maximum and minimum possible value of P(AIB) and P(AUB)? e) [5 pts] Compare P(A|B) and P(A), is the former greater or less than, or equal to the latter? f) [5 pts] What is the probability density function for Gaussian distribution? g) [5 pts] Let random variable X be the outcome of a roll of a six-sided die (a fair one, therefore all six sides are equally likely). What is the expectation of X? 3.2. Linear algebra a) [5 pts] =312a =241b what is the dot product of them (i.e., baT)? b) [15 pts] Consider dRx∈ and some dRu ∈ with 1=u. What is the maximum value of xuT? minimum value of xuT? minimum value of || xuT? 3.3. Calculus a) [5 pts] Let xxeexf+=1)( , what is dxxdf )(? b) [5 pts] Let 22)3ln(),(xyxeyeyxf ++=, what is yyxf∂∂),(? c) [10 pts] Assume a>0, b>0, find xxxbeae2min−+.How to submit your homework? • Please either submit the electronic version of your homework via eLearning, or submit the hard copy in class. • Please write your answers clearly. • Please remember to write down your
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