Define a random process ✗(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(-λ), (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. function of Seess (c) What is E[X(t)]?
Define a random process ✗(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(-λ), (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. function of Seess (c) What is E[X(t)]?
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![Define a random process ✗(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(-λ), (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.
function of
Seess
(c) What is E[X(t)]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2F286e147c-a96d-4d87-ba2b-a9211948f569%2Fwrtwtp_processed.png&w=3840&q=75)
Transcribed Image Text:Define a random process ✗(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(-λ), (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.
function of
Seess
(c) What is E[X(t)]?
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