Define a random process X(t) as follows: (1) X(t) assumes only one of two possible levels 1 or -1 at any time, (2) X(t) switches back and forth between its two levels randomly with time, (3) the number of level transitions in any time interval is a Poisson random variable, that is, the probability of exactly k transitions, when the average rate of transitions is λ, is given by [(t)/k!] exp(-), (4) transitions occurring in any time interval are sta- tistically independent of transitions in any other interval, and (5) the levels at the start of any interval are equally probable. X(t) is usually called the random telegraph process. It is an example of a discrete random process. lation function of the precess. (d) Discuss the stationarity of X(t).
Define a random process X(t) as follows: (1) X(t) assumes only one of two possible levels 1 or -1 at any time, (2) X(t) switches back and forth between its two levels randomly with time, (3) the number of level transitions in any time interval is a Poisson random variable, that is, the probability of exactly k transitions, when the average rate of transitions is λ, is given by [(t)/k!] exp(-), (4) transitions occurring in any time interval are sta- tistically independent of transitions in any other interval, and (5) the levels at the start of any interval are equally probable. X(t) is usually called the random telegraph process. It is an example of a discrete random process. lation function of the precess. (d) Discuss the stationarity of X(t).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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