Question: Find the average error probability in Problem 13. Problem 13 Suppose that the random variable X is transmitted over a communication channel. Assume that the

Find the average error probability in Problem 13.

Problem 13

Suppose that the random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = 2X +W, where W ∼ N(0,σ²) is independent of X. Suppose that X = 1 with probability p, and X = −1 with probability 1 −p. The goal is to decide between X = −1 and X = 1 by observing the random variable Y . Find the MAP test for this problem.

Step by Step Solution

★★★★★

3.45 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To find the Maximum A Posteriori MAP decision rule we need to determine the decision boundary that maximizes the posterior probability of the transmit... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Introduction To Probability Statistics Questions!

Find the average error probability in Example 9.10 Example 9.10 Suppose that t he random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = X +W,...

Suppose that t he random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = X +W, where W N(0, 2 ) is independent of X. Suppose that X = 1 with...

Suppose that the signal X N(0, 2 X ) is transmitted over a communication channel. Assume that the received signal is given by Y = X +W,where W N(0, 2 W ) is independent of X. 1. Find the ML...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Suppose that the random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = 2X +W, where W N(0, 2 ) is independent of X. Suppose that X = 1 with...

PA 818 Professor Wallace Fall 2016 Homework #5 (Due Nov 9 and 10 in Sections) 1. Shoes Fight. A local newspaper, The Garlic, claims that an average area man owns fewer than 5 pairs of shoes. Your...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

geometric, poisson probability, 7:067 Q SGE all 7:07 Q SGE all 2. [-/3 Points] DETAILS BBUNDERSTAT12 5.4.014.M 4. [-/2 Points] DETAILS BBUNDERSTAT12 5.4.016. MY NOTES ASK YOUR TEACHER PRACTICE...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Carefully study the Income Statement of Target Corporation and its accompanying notes. In your opinion, which items would you have difficulty accepting as an analyst interested in predicting the...

The U.S. Department of Agriculture (USDA) Center for Nutrition Policy and Promotion (CNPP) developed and administered the Healthy Eating Index-2005 to measure how well the population follows the...

At what yield will the bonds be issued? 0 . 5 7 % 0 . 4 5 % 0 . 5 2 % 0 . 5 % 0 . 6 4 %

How did his behavior change over time?

A box contains 3 red balls and 2 yellow balls. Give a suitable sample space to describe all possible outcomes for the experiment of selecting 4 balls at random, in each of the following schemes: (i)...

Irne has four books that she wants to put on a library shelf. Three of these books form a 3-volume set of a dictionary, so that they are marked as Volumes I, II, and III, respectively. (i) Find an...

Mary has in her wallet three $1 coins, one $2 coin and four coins of 25 . She selects four coins at random from her wallet. (i) Write down a sample space for the possible selections she can make....

2- Name and Discuss 2 different types of Committeesthat an organization sets up.

Which of the following are elements of good netiquette? [Select all that apply]Can choose more than one answers 1.Stay on topic 2.Never raise objections to others' ideas in order to protect their...

Labor Economics(10) Is the following statement true or false? "A wage subsidy given to firms for hiring high-skilled workers by the government reduces firms' demand for low-skilled workers through...