Homework 8, due Monday March 21, 2016

  • Based on the table of number of births each month in the US (for example, birth-data), estimate the entropy of a random variable taking values in days of the year, with probabilities according to the frequency of the birthday).
  • Based on a  table of letter frequencies in the English language, estimate the entropy of the English language, checking the answer from page 276.  (Just use single letter frequencies from table 1.3 on page 6.  More accurate measures of the entropy are possible, but are not necessary for this exercise.)
  • We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the others.  Locate the counterfeit coin by using four weighings on a pan balance.  Explain in terms of entropy.
  • 5.45 Warning: perfect secrecy is a condition that must hold for all c in C and all m in M.
  • 5.46
  • 5.56(a)