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This problem was taken from Schaumburg probability random variables and random processes, The answers are given, please show how to get to those answers, thank you 5.85. Suppose that a random process X() is wide-sense stationary with autocorrelation (a) Find the second moment of the r.v. X(5) (b) Find the second moment of the r.v. X(5 )- x(3). 5.85. (a) EX(5)]=1; (b) EIX(5)-X(3)]2} = 2(1-e-1)
Three random variables A, B, and C and 1. The random processes X(t) and Y (t) answer the questions below. (24 points) independent identically distributed (id) uniformly between are defined by the given equations. Use this information to are X(t) = At + B Y(t) = At + C (a) Find the autocorrelation function between X(t) and Y(t) (b) Find the autocovariance function between X (t) and Y(t). (c) Are X(t) and Y(t) correlated random processes? Three random variables A,...
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
Random assortment of chromosomes is one of the processes by which genetic variation is generated. Explain what the process means and how new variation is produced as a consequence of random assortment.
Production Line Simulation Random variation is an important part of most processes in operations and supply chain management. For example, customer demand, supplier lead time, answering a customer inquiry, or processing a batch of material at a machining center all vary from customer to customer, delivery to delivery, and batch to batch. As the chapter notes, simulation allows us to model randomness. Although most large-scale simulations are done on computers using random numbers, there are other ways to generate random...
Another employee has collected a random sample of data from one of your processes and calculated two Confidence Intervals which are: (172.52, 196.48) and (174.45, 194.55). (a) What is the value of the sample mean? (b) One of these intervals is a 90% CI and the other is a 95% CI. Which one is the 95% Cl and why? Another employee has collected a random sample of data from one of your processes and calculated two Confidence Intervals which are:...
Probability and Random Processes for Engineers You roll a fair die twice: all 36 outcomes are equally likely. Let A be the event that the first roll is 1, 2, or 3. Let B be the event that the second roll is 6. Finally, let C be the event that the sum of the rolls is even. (a) Show that any two of A, B, and C are independent (b) Are A, B, and C independent? Derive your answer two...
Problem 3 for subject of Random Processes 3. Calculate the correlation co-efficient coefficient for the following data: X:65 66 67 67 68 69 70 72 Y:67 68 65 68 72 72 69 71