2. (a) Let {Xt} be the process nt + B sin 6 at Xt = A cos t = 0,±1, ., 6 where A and B are uncorrelated normal random variables with mean 0 and variance 2. Find the best estimate of X5 in terms of X3 and X4. (b) Let X1, X2, X4, X5 be observations from the MA(1) model Xt = Zt – 2Zt-1, {Z}} ~ WN(0, 2). Find the best linear estimate of X3 in terms of X1, X2 and X5 and find its mean squared error.

2. (a) Let {Xt} be the process nt + B sin 6 at Xt = A cos t = 0,±1, ., 6 where A and B are uncorrelated normal random variables with mean 0 and variance 2. Find the best estimate of X5 in terms of X3 and X4. (b) Let X1, X2, X4, X5 be observations from the MA(1) model Xt = Zt – 2Zt-1, {Z}} ~ WN(0, 2). Find the best linear estimate of X3 in terms of X1, X2 and X5 and find its mean squared error.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

2. (a) Let {Xt} be the process
()
at
+ B sin
6
X1 = A cos
t = 0,±1, . .,
where A and B are uncorrelated normal random variables with mean 0 and variance 2. Find
the best estimate of X5 in terms of X3 and X4.
(b) Let X1, X2, X4, X5 be observations from the MA(1) model
Xt = Zt – 2Zt-1, {Zt}~ WN(0, 2).
Find the best linear estimate of X3 in terms of X1, X2 and X5 and find its mean squared
error.

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