How well a model can describe a source

Question

Response to the following problem:

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) F_x(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(x_k - 1) _x(x_k). Compare your results with those of part (a).

(c) Repeat (b) using a single-letter context.

(d) Repeat (b) using a two-letter context.