<:> Exercises
- Generate a 1st order Markov model for the sequence: `x z z y x x z y'
- Use the 1st order model to generate a new sequence that is
at least twice the length of the original.
- Specify a sequence whose 1st order Markov model might yield
the chain `a b b a'. The sequence you specify must be
something other than `a b b a'.
- The following text is a word-level Markov text: guess it's origin and
order. `Nevertheless the centurion saw what was I ever wont to haunt.
Now the body of his handmaiden: for, behold, your sheaves stood round
about.'
- Let's say we use the chain-rule to discover the 3rd-order n-gram
probabilities for a certain text. If the text is 1000 words long and
contains 50 different words, how many multiplications should we expect
to do and why?
- With what probability does the Java random number generator produce a
value in the range 0.4-0.6?
- What will be the effect if an ordinary random-number generator (i.e.,
one which generates all values with equal probability) is used in the
Meservy and Fadel method of text-generation?
- What types of music do you think will be most easily generated
using Markov-chain methods?
- To improve the syntactic coherence of text generated from a
Markov model we should use higher-order statistics. Will this also
help to improve semantic coherence?