Problem Set #6
ENEE 426, Spring 2008
Due: Monday, May 11
Complete the following problems:
1. Compute the entropy of the following random variables: (5 pts)
a. The roll of a die – Pr[X={1, 2, …, 6}] = 1/6
b. A biased coin – Pr[X=heads]=3/4; Pr[X=tails]=1/4
2. Compute the entropy of characters from the English alphabet. Use the character frequencies
listed on the Wikipedia entry: http://en.wikipedia.org/wiki/English_alphabet (10 pts)
3. Develop a Huffman Code to optimally encode the alphabet from #2. (10 pts)
4. Suggest a way to achieve better compression of English text over using Huffman codes on a per-
character alphabet, which has an actual entropy of around 4.7 bits per character (smaller than
the number found in #2). (5 pts)
5. What properties of WiFi make MAC-layer encryption more necessary than in a wired Ethernet
network? (5 pts)
6. Describe possible attacks that could be occurring if you visit a website whose certificate is
invalid? (5 pts)
Complete the following additional problem (50 points):
1. Complete Laboratory 9, “Queuing Disciplines”, from the Network Simulations Experiment
Manual
a. Turn in a lab report, as described in the manual, that includes the answers to the
questions and graphs generated during the experiments
2. Extra Credit: Complete Laboratory 10 for 50 extra credit points