Free choice homework (no need to deliver):
- Derive the corollaries on lecture slide 8, the chain rule on slide 9 and the partition
rule on slide 10. Use only the axioms and set theory to do the derivation.
- Let a ``word" be defined as a sequence of symbols separated by white-space.
Take a large English text (for example a collection containing at least 1 million word
occurences from Wikipedia) and extract all words
and their counts from a steadily growing part of the text. To do so, start with 10%
of the text and add another 10% every time until you have the full text to do the
counting.
Plot the relative frequency estimate (RFE) of the word probability for certain words
(e.g. ``the" or ``man" or ``company" or ``browsing" or ``Bush") and observe whether the
RFE is converging around a certain value as the data grows large. Discuss the differences
between the convergence of different words with your fellow colleagues.
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