PURPOSE: Understand Markov chains as a means to model/predict probabilistic processes in a simple case.

a. Toss a coin 32 times and record the outcome (as a string of H and T).

b. Compute the experimentally observed probability of heads over tosses 2 through 21, inclusive (20 outcomes).

c. Compute the Markov chain transition probabilities over the first 21 tosses (viz., the first 20 transitions).

d. Repeat (a)-(c) above with a sequence verbally derived from a friend not in the class who does not know the underlying model you are trying to construct.

e. Using any language you wish, implement a computer program that uses the Markov chain model to predict the final ten transitions of each data set (throws 23-32 given the values of throws 22-31, respectively). That is, given the previous state (throw i), compute the next state (throw i+1) using the model, compare with the actual data, and tally the error function (# of wrong guesses).