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2. Let (et) be a zero mean white noise process with variance 1. Suppose that the...
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the...
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the observed process is k = et + 0.5e-2. a. Explain why {Yt) is stationary. b. Compute yo-V(Y.) c. Compute the autocorrelation pkY, kl-0,1,2,... for Y) d. Let Wt = 3 + 4t + h. i. Find the mean of {W) ii. Is W3 stationary? Why or why not? iii. Let Z Vw, W,- W,_1. Is {Z.1 stationary? Why or why not?
Let Wt de a (Gaussian) white noise with variance σ 2 . Then, let Xt =...
Let Wt de a (Gaussian) white noise with variance σ 2 . Then, let
Xt = WtWt−1 + µ, where µ is a real constant. Determine the mean and
autocovariance of (Xt)? Is this process stationary?
Let W, de a (Gaussian) white noise with variance σ2. Then, let of where μ is a real constant. Determine the mean and (X)? Is this process stationary?
Consider the process Y.-μ + et-o, et-1-912 et-12, where {ed denotes a white-noise process with mean...
Consider the process Y.-μ + et-o, et-1-912 et-12, where {ed denotes a white-noise process with mean 0 and variance σ? > 0. Assume that et ls independent of Yt-1, Yt-2, Find the autocorrelation function for (Yt).
2.4 Let (e) be a zero mean white noise process. Suppose that the observed process is...
2.4 Let (e) be a zero mean white noise process. Suppose that the observed process is Y = e, + 0,-1, where is either 3 or 1/3. (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of and that the autocorrelation functions are the same for 0 = 3 and 0 = 1/3. For simplicity, suppose that...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et)...
Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et) = σe2 and Cov(et, es) = 0 for t ≠ s. Define a new time series {Yt} by Yt = et + 0.6 et -- 1 – 0.4 et – 2 + 0.2 et – 3. 1. Find E(Yt ) and Var(Yt ). 2. Find Cov(Yt , Yt – k) for k = 1, 2, ...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.?...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.? Explain b) Is X stationary? Explain c) Calculate the mean, variance, and autocorrelation function of X d) How does the answer you obtained in (c) compare with the mean, variance and autocor- relation function of Y?
2. Suppose that Ya ut where the...
Let Xn, -inf to +inf be a discrete-time zero-mean white noise process, i.e., μx[n] = 0, Rx[n] =δ[...
Let Xn, -inf to +inf be a discrete-time zero-mean white noise
process, i.e., μx[n] = 0, Rx[n] =δ[n]. The process is filtered
using an LTI system with impulse response
h[n] =αδ[n] + βδ[n−1].
Find α and β such that the output process Yn has autocorrelation
function Ry[n] =δ[n+1] + 2δ[n] +δ[n−1].
5) (3 points) Let Xn, -o0 K n oo, be a discrete-time zero-mean white noise process, i.e, ,1z[n]-(), Rx [n] S[n]. The process is filtered using an LTI system...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Y0 = ceo and Y1-CgY0-ei. Then let Y,-φ1Yt-it wt-1-et for t > ï as in an AR(2) process. Show that the process mean, E(Y.), is zero. (b) Suppose that (a is generated according to }.-10 e,-tet-+扣-1 with e,-N(0.) 0 Find the mean and covariance functions for (Y). Is (Y) stationary? Justify your...
: Assume Yt is a time series process and Et is a white noise process with...
: Assume Yt is a time series process and Et is a white noise process with mean zero and constant variance. (a). Write an equation for AR(4) process. (b). Write an equation for AR(5) process. (c). Write an equation for MA(3) process. (d). Write down an equation for MA(2) process. (e). Write an equation for ARMA (4,2) process. (f). Do more research and write an equation for ARIMA (4,0,2) proce
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the observed process is k = et + 0.5e-2. a. Explain why {Yt) is stationary. b. Compute yo-V(Y.) c. Compute the autocorrelation pkY, kl-0,1,2,... for Y) d. Let Wt = 3 + 4t + h. i. Find the mean of {W) ii. Is W3 stationary? Why or why not? iii. Let Z Vw, W,- W,_1. Is {Z.1 stationary? Why or why not?
Let Wt de a (Gaussian) white noise with variance σ 2 . Then, let
Xt = WtWt−1 + µ, where µ is a real constant. Determine the mean and
autocovariance of (Xt)? Is this process stationary?
Let W, de a (Gaussian) white noise with variance σ2. Then, let of where μ is a real constant. Determine the mean and (X)? Is this process stationary?
Consider the process Y.-μ + et-o, et-1-912 et-12, where {ed denotes a white-noise process with mean 0 and variance σ? > 0. Assume that et ls independent of Yt-1, Yt-2, Find the autocorrelation function for (Yt).
2.4 Let (e) be a zero mean white noise process. Suppose that the observed process is Y = e, + 0,-1, where is either 3 or 1/3. (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of and that the autocorrelation functions are the same for 0 = 3 and 0 = 1/3. For simplicity, suppose that...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.? Explain b) Is X stationary? Explain c) Calculate the mean, variance, and autocorrelation function of X d) How does the answer you obtained in (c) compare with the mean, variance and autocor- relation function of Y?
2. Suppose that Ya ut where the...
Let Xn, -inf to +inf be a discrete-time zero-mean white noise
process, i.e., μx[n] = 0, Rx[n] =δ[n]. The process is filtered
using an LTI system with impulse response
h[n] =αδ[n] + βδ[n−1].
Find α and β such that the output process Yn has autocorrelation
function Ry[n] =δ[n+1] + 2δ[n] +δ[n−1].
5) (3 points) Let Xn, -o0 K n oo, be a discrete-time zero-mean white noise process, i.e, ,1z[n]-(), Rx [n] S[n]. The process is filtered using an LTI system...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Y0 = ceo and Y1-CgY0-ei. Then let Y,-φ1Yt-it wt-1-et for t > ï as in an AR(2) process. Show that the process mean, E(Y.), is zero. (b) Suppose that (a is generated according to }.-10 e,-tet-+扣-1 with e,-N(0.) 0 Find the mean and covariance functions for (Y). Is (Y) stationary? Justify your...
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