Makeup Second Examination
CLOSED BOOK, NO NOTES, CALCULATORS, OR SCRAP PAPER. TURN OFF CELLPHONES.
ALLOTTED TIME IS 1 hour and 30 min.
SHOW YOUR WORK, GIVE REASONS, NOT JUST ANSWERS.
Place your three-digit ID number, not your name, on each sheet.
Work each problem on a separate sheet of paper so that the
individual questions can be separated for grading.
1. Consider a source with ﬁve symbols
ing probabilities of being chosen of
16. Consider a
preﬁx code for this set of symbols with the corresponding codewords being
(a)(2pts) What is the expected codeword length?
(b)(3pts) Calculate the source entropy
(c)(4pts) Construct a Huﬀman code for this source, evaluate its expected
length, and compare it to the entropy found in (b).
(d)(6pts) Consider the set of codewords [00
1] for the symbols
listed in (a). Evaluate the expected codeword length and compare it to the