Problem 2 Are the following processes stationary in the wide sense? Are they erg

Question

Problem 2 Are the following processes stationary in the wide sense? Are they ergodic? Circle, and explain your answers. a) The random process X(t)-Acos(t) where A is a Gaussian random variable with E[A]-2 and 6. Wide sense stationary? Yes or no? Explain. Ergodic: Yes or no? Explain. b) The random process Y (t) represents amount of gas in the tank of a car vs. time. Each sample function represents the gas vs. time after a different stop to refill the gas Wide sense stationary? Yes or no? Explain. Ergodic: Yes or no? Explain. c) The random process Z(t) the number of people in line at a grocery store vs. time. Each sample function represents the people vs. time for a different cashier station. Wide Sense Stationary? Yes or no? Explain. Ergodic? Yes or no? Explain

Explanation / Answer

a)The random process X(t) =Acos(t) is a stationary process because A is a Gaussian random variable.

Yes it is Ergodic because it is non null recurrent,aperiodic .

b)The random process Y(t) is a continuous so it has index set an also with continuous state space.It is a stationary process and also ergodic.

c)The random process Z(t) is a stationary process with discrete state space with contious index set .It is Ergodic because it is non null recurrent,aperiodic.

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