# Question: A random waveform is generated as follows The waveform starts

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 - 1 volt with probability q = 1 –p. 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.

(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.

**View Solution:**## Answer to relevant Questions

A student takes this course at period 1 on Monday, Wednesday, and Friday. Period 1 starts at 7: 25 A. M. Consequently, the student sometimes misses class. The student’s attendance behavior is such that she attends class ...Define the generating functions (a) Show that Pi, j(z) = Fi, j(z) Pjj(z). (b) Prove that if state j is a transient state, then for all i, Suppose we label the spaces on a monopoly board as {0, 1, 2… 39} where, 0 = Go, 1 = Mediterranean Ave., 2 = Community Chest, 3 = Baltic Ave., ... 39 = Boardwalk. Let X [k] be the location of a player after k turns. ...Let be a deterministic periodic waveform with period to. A random process is constructed according to X (t) = s (t – T) Where T is a random variable uniformly distributed over [0, to]. Show that the random process X (t) ...Find the PSD of the process Let Wn be an IID sequence of zero- mean Gaussian random variables with variance. Define a discrete- time random process, X[ n] = pX[ n – 1]+ Wn, n = 1, 2, 3, … where X[ 0] = W0 and is a ...Post your question