ps1 - Problem Set 1 MAS 622J/1.126J: Pattern Recognition...

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Problem Set 1 MAS 622J/1.126J: Pattern Recognition and Analysis Due Monday, 18 September 2006 [Note: All instructions to plot data or write a program should be carried out us- ing either Python accompanied by the matplotlib package or Matlab. Feel free to use either or both, but in order to maintain a reasonable level of consistency and simplicity we ask that you do not use other software tools.] Problem 1: Why? a. Describe an application of pattern recognition related to your research. What are the features? What is the decision to be made? Speculate on how one might solve the problem. Limit your answer to a page. b. In the same way, describe an application of pattern recognition you would be interested in pursuing for fun in your life outside of work. X Problem 2: Probability Warm-Up Let X and Y be random variables. Let µ X E[ X ] denote the expected value of X and σ 2 E[( X µ X ) 2 ] denote the variance of X . Use excruciating detail to answer the following: a. Show E[ X + Y ] = E[ X ] + E[ Y ]. X b. Show σ 2 = E[ X 2 ] µ 2 . X 2 are uncorrelated, then σ Z c. Show that independent implies uncorrelated. d.
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ps1 - Problem Set 1 MAS 622J/1.126J: Pattern Recognition...

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