4. Estimation based on a function of the observation. Let O be a positive random variable, with known mean and variance o?, to be estimated on the basis of a measurement X of the form X = vew. We assume that W is independent of e with zero mean, unit variance, and known fourth moment E[W]. Thus, the conditional mean and variance of X given e are 0 and 0, respectively, so we are essentially trying to estimate the variance of X given an observed value. %3D (a) Find the linear LMS estimator of e based on X = r. (b) Let Y = X². Find the linear LMS estimator of e based on Y = y.
4. Estimation based on a function of the observation. Let O be a positive random variable, with known mean and variance o?, to be estimated on the basis of a measurement X of the form X = vew. We assume that W is independent of e with zero mean, unit variance, and known fourth moment E[W]. Thus, the conditional mean and variance of X given e are 0 and 0, respectively, so we are essentially trying to estimate the variance of X given an observed value. %3D (a) Find the linear LMS estimator of e based on X = r. (b) Let Y = X². Find the linear LMS estimator of e based on Y = y.
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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![4. Estimation based on a function of the observation. Let e be a positive random variable, with
known mean p and variance o?, to be estimated on the basis of a measurement X of the
form X = vOW. We assume that W is independent of e with zero mean, unit variance,
and known fourth moment E[W4]. Thus, the conditional mean and variance of X given O
are 0 and 0, respectively, so we are essentially trying to estimate the variance of X given an
observed value.
(a) Find the linear LMS estimator of e based on X = x.
(b) Let Y = X?. Find the linear LMS estimator of O based on Y = y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8aa7df1-1bb0-4047-818e-7f32a6ce9d33%2Fde82d796-5229-4037-8675-cecf27f45e9f%2F4fjcdcq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Estimation based on a function of the observation. Let e be a positive random variable, with
known mean p and variance o?, to be estimated on the basis of a measurement X of the
form X = vOW. We assume that W is independent of e with zero mean, unit variance,
and known fourth moment E[W4]. Thus, the conditional mean and variance of X given O
are 0 and 0, respectively, so we are essentially trying to estimate the variance of X given an
observed value.
(a) Find the linear LMS estimator of e based on X = x.
(b) Let Y = X?. Find the linear LMS estimator of O based on Y = y.
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