Consider the problem of sending a binary message, 0 or 1, through a signal

channel consisting of several stages, where transition through each stage is subject

to a fixed probability of error ®. Suppose that X0 = 0 is the signal that is sent

and let Xn be the signal that is received at the nth stage. Assume that X is a

Markov chain with transition probabilities

Determine P(X0 = 0; X1 = 0; X2 = 0), the probability that no error occurs

up to stage 2.

channel consisting of several stages, where transition through each stage is subject

to a fixed probability of error ®. Suppose that X0 = 0 is the signal that is sent

and let Xn be the signal that is received at the nth stage. Assume that X is a

Markov chain with transition probabilities

Determine P(X0 = 0; X1 = 0; X2 = 0), the probability that no error occurs

up to stage 2.