Chapter 8.1, Problem 2CYU

Learning Process An elementary learning process consists of subjects participating in a sequence of events. Experiment shows that, of the subjects not conditioned to make the correct response at the beginning of any event, 40% will be conditioned to make the correct response at the end of the event. Once a subject is conditioned to make the correct response, they stay conditioned.

a. Set up the $2\times 2$ stochastic matrix with columns and rows labeled N (not conditioned) and C (conditioned) that describes this situation.

b. Compute $A^3$.

c. If, initially, all the subjects are not conditioned, what percent of them will be conditioned after three events?