A PCM waveform has the two states +1 and 0. Suppose the transition matrix is
The initial value of the waveform is determined by the flip of a coin, with the outcome of a head corresponding to +1 and a tail to 0.
(a) What is the probability that the waveform will be at +1 after one step if the coin is a fair coin?
(b) Find the same probability if the coin is biased such that a head occurs with probability.
(c) Repeat the problem for two steps.