/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 4.43 A communications channel transmi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 4.43 (page 166)

A communications channel transmits the digits 0and 1. However, due to static, the digit transmitted is incorrectly received with probability 2. Suppose that we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we transmit 00000 instead of 0 and 11111 instead of 1. If the receiver of the message uses 鈥渕ajority鈥� decoding, what is the probability that the message will be wrong when decoded? What independence assumptions are you making?

Short Answer

Expert verified

The probability that the message is wrong when decoded is0.0579.

Step by step solution

01

Given Information

The probability that the digit transmitted incorrectly is, 0.2.

To reduce the chance of error 5digits are transmitted instead of 1digits.

The message is wrongly received when an3,4or5digits are transmitted incorrectly.

02

Solution of the Problem

The probability that the message will be wrong when decoded is,

P(Wrongmessage)=P(X鈮�3)

=53(0.2)3(0.8)2+54(0.2)4(0.8)1+55(0.2)5(0.8)0

=0.0512+0.0064+0.0003

We get,

=0.0579.

03

Final Answer

The probability that the message is wrong when decoded is0.0579.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The National Basketball Association (NBA) draft lottery involves the 11 teams that had the worst won-lost records during the year. A total of 66 balls are placed in an urn. Each of these balls is inscribed with the name of a team: Eleven have the name of the team with the worst record, 10 have the name of the team with the second worst record, 9 have the name of the team with the third worst record, and so on (with 1 ball having the name of the team with the 11 th-worst record). A ball is then chosen at random, and the team whose name is on the ball is given the first pick in the draft of players about to enter the league. Another ball is then chosen, and if it "belongs" to a team different from the one that received the first draft pick, then the team to which it belongs receives the second draft pick. (If the ball belongs to the team receiving the first pick, then it is discarded and another one is chosen; this continues until the ball of another team is chosen.) Finally, another ball is chosen, and the team named on the ball (provided that it is different from the previous two teams) receives the third draft pick. The remaining draft picks 4 through 11 are then awarded to the 8 teams that did not "win the lottery," in inverse order of their won-lost not receive any of the 3 lottery picks, then that team would receive the fourth draft pick. Let X denote the draft pick of the team with the worst record. Find the probability mass function of X.

A fair coin is flipped 10times. Find the probability that there is a string of 4consecutive heads by

(a) using the formula derived in the text;

(b) using the recursive equations derived in the text.

(c) Compare your answer with that given by the Poisson approximation.

In Problem 4.5,for n=3,if the coin is assumed fair, what are the probabilities associated with the values that X can take on?

To determine whether they have a certain disease, 100people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to place the people into groups of 10. The blood samples of the 10people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 10people, whereas if the test is positive, each of the 10people will also be individually tested and, in all, 11tests will be made on this group. Assume that the probability that a person has the disease isrole="math" localid="1646542351988" .1 for all people, independently of one another, and compute the expected number of tests necessary for each group. (Note that we are assuming that the pooled test will be positive if at least one person in the pool has the disease.)

Suppose that the random variable Xis equal to the number of hits obtained by a certain baseball player in his next 3at-bats. If P{X=1}=3,P{X=2}=2andP{X=0}=3P{X=3}, find E[X].
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.