Suppose that a communications network transmits binary

digits, 0 or 1, where each digit is transmitted 10 times in succession.

During each transmission, the probability is 0.995 that the

digit entered will be transmitted accurately. In other words, the

probability is 0.005 that the digit being transmitted will be

recorded with the opposite value at the end of the transmission.

For each transmission after the first one, the digit entered for transmission

is the one that was recorded at the end of the preceding

transmission. If X0 denotes the binary digit entering the system,

X1 the binary digit recorded after the first transmission, X2 the binary

digit recorded after the second transmission, . . . , then {Xn}

is a Markov chain.

(a) Construct the (one-step) transition matrix.

(b) Use your IOR Tutorial to find the 10-step transition matrix

P(10). Use this result to identify the probability that a digit

entering the network will be recorded accurately after the

last transmission