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Question 8 Consider the following graphs, where the left plot is the likelihood fx|e(x|0), and the right plot is the prior fo(0). The random variable X denotes the observation. Find the MAP estimate of 0. fx|e(x|0) fe(0) 0.5 0.5 0.4 0.4 - 0.3 0.3 - 0.2 0.2 0.1 0.1 1 2 3 4 1 2 3 4

Question 8 Consider the following graphs, where the left plot is the likelihood fx|e(x|0), and the right plot is the prior fo(0). The random variable X denotes the observation. Find the MAP estimate of 0. fx|e(x|0) fe(0) 0.5 0.5 0.4 0.4 - 0.3 0.3 - 0.2 0.2 0.1 0.1 1 2 3 4 1 2 3 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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Question 8 Consider the following graphs, where the left plot is the likelihood fx|e(x|0), and the right plot is the prior fo(0). The random variable X denotes the observation. Find the MAP estimate of 0. fx|e(x|0) fe(0) 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 1 2 3 4 5 1 2 3 4 5
Transcribed Image Text:Question 8 Consider the following graphs, where the left plot is the likelihood fx|e(x|0), and the right plot is the prior fo(0). The random variable X denotes the observation. Find the MAP estimate of 0. fx|e(x|0) fe(0) 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 1 2 3 4 5 1 2 3 4 5
Question 10 In this question we explore the application of MAP and LMS estimation in a communication channel. Suppose we want to send a signal X, but this is corrupted by additive noise N such that the signal at the receiver is Y, where Y = X+ N. We assume the noise is Gaussian with zero mean and a known variance, i.e., N ~ N(0, 0²). We further assume that X is a continuous random variable with half of the probability clustered at +1 and half of the probability clustered at –1. (We say this, instead of calling X a discrete random variable, is so that the estimate does not necessarily have to be ±1. We can formalize it in more rigorous mathematics using a delta function, but that is beyond the scope of this class.) 1. Find the MAP estimate of X. 2. Find the LMS estimate of X.
Transcribed Image Text:Question 10 In this question we explore the application of MAP and LMS estimation in a communication channel. Suppose we want to send a signal X, but this is corrupted by additive noise N such that the signal at the receiver is Y, where Y = X+ N. We assume the noise is Gaussian with zero mean and a known variance, i.e., N ~ N(0, 0²). We further assume that X is a continuous random variable with half of the probability clustered at +1 and half of the probability clustered at –1. (We say this, instead of calling X a discrete random variable, is so that the estimate does not necessarily have to be ±1. We can formalize it in more rigorous mathematics using a delta function, but that is beyond the scope of this class.) 1. Find the MAP estimate of X. 2. Find the LMS estimate of X.
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