Unit 4: Probability

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Probability is nothing but common sense reduced to calculation. (Pierre-Simon Laplace, 1749 - 1827)

Schedule

  • Lecture 4
  • Recitation 5

Lecture Handouts

  • Lecture Notes - Chapter 5: Probability (PDF)
  • Towser's Wonderland Park greyhound handicaps, Boston Globe, March 4, 2002
  • Part of Table of letter frequency in English (from A Tale of Two Cities)
  • Huffmann, David A. A Method for the Construction of Minimum-Redundancy Codes. Proc IRE 40, no. 9 (September 1952): 1098-1101.
  • Page 13 of C. E. Shannon, "A Mathematical Theory of Communication."

Assignment

  • Problem Set 4 (PDF)
  • Problem Set 4 Solutions (PDF)

Resources

Technical

  • Salomon, David. "Huffman coding," and "Facsimile Compression using Huffman coding." Section 2.8 and Section 2.13 in Data Compression. Springer; 1997. ISBN: 0387982809.
  • MIT student enrollment data: Y chart (all students) . . . Women students
  • Probability Tutorial. "Statistics for Engineers: Introduction to Probability Theory," from University of Wollongong, Australia.

Historical

General Technical Books

There are many excellent texts on probability, many of which do not assume a familiarity with mathematics beyond introductory calculus. Most books on communications include a summary of the necessary background in probability.

  • Drake, Alvin W. Fundamentals of Applied Probability Theory. New York, NY: McGraw-Hill, Inc., 1967; reprinted 1988. ISBN: 0070178151.
    Prof. Drake taught 6.041 Probabilistic Systems Analysis for many years until he retired recently
  • Applebaum, David. Probability and Information. Cambridge, UK: Cambridge University Press, 1996. ISBN: 0521555280.
    Chapter 4, Probability, contains a good comparison of the different philosophies underlying probability (symmetry, subjective, frequency)
  • Haykin, Simon. "Appendix 1: Probability Theory." In Communication Systems. 4th ed. New York, NY: John Wiley and Sons, Inc., 2001. ISBN: 047140182X.

There are many excellent texts on coding theory and communications, most of which assume a familiarity with mathematics beyond introductory calculus.

  • Pierce, John R. An Introduction to Information Theory: Symbols, Signals, and Noise. 2nd ed. New York, NY: Dover Publications, Inc., 1961, 1980. ISBN: 0486240614.
    Mostly nonmathematical, by one of the nation's great scientific contributors at AT&T Bell Laboratories, who was also interested in reaching a general audience. He was later on the faculty at Caltech. One of his interesting sideline activities was writing science fiction stories under the pen name J. J. Coupling. He died April 2, 2002 at the age of 92
  • Gallager, Robert G. Information Theory and Reliable Communications. New York, NY: John Wiley & Sons, Inc., 1968. ISBN: 0471290483.
    One of the early textbooks, designed for first-year graduate students, by one of the pioneers in communications, an MIT faculty member, later awarded the IEEE Medal of Honor, its most prestigious award
  • Cover, Thomas M., and Joy A. Thomas. Elements of Information Theory. New York, NY: John Wiley & Sons, Inc., 1991. ISBN: 0471062596.
    Aimed at university seniors and first-year graduate students. One of several excellent books of that era. Professor Cover, at Stanford University, is one of the leaders in Information Theory

Laboratory