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Conduct an experiment to see how well a model can describe a source.
(a) Write a program that randomly selects letters from the 26-letter alphabet [a,b,..., z} and forms four-letter words. Form 100 such words and see how many of these words make sense.
(b) Among the accompanying data sets is a file called 4letter.words, which contains a list of four-letter words. Using this file, obtain a probability model for the alphabet. Now repeat part (a) generating the words using the probability model. To pick letters according to a probability model, construct the cumulative density function (cdf) Fx(x) (see Appendix A for the definition of cdf). Using a uniform pseudorandom number generator to generate a value r, where 0 1 if Fx(xk - 1) x(xk). Compare your results with those of part (a).
(c) Repeat (b) using a single-letter context.
(d) Repeat (b) using a two-letter context.
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