A random waveform is generated as follows. The waveform starts at 0 voltage. Every seconds, the waveform switches to a new voltage level. If the waveform is at a voltage level of 0 volts, it may move to +1 volt with probability or it may move to + volt with probability . Once the waveform is at +1 (or -1), the waveform will return (with probability 1) to 0 volts at the next switching instant.
(a) Model this process as a Markov chain. Describe the states of the system and give the transition probability matrix.
(b) Determine whether each state is periodic or aperiodic. If periodic, determine the period of each state.
(c) For each instant of time, determine the PMF for the value of the waveform.