### Binary Symmetric Channel Analysis#### Question 15:The figure below illustrates a binary symmetric channel where each symbol ("0" or "1") sent is inverted with probability "p", independently of all other symbols. In simple terms:- When "0" is transmitted, the probability of receiving "1" is "p" and the probability of receiving "0" is "1-p".- When "1" is transmitted, the probability of receiving "0" is "p" and the probability of receiving "1" is "1-p".The input \(X\) to the binary symmetric channel shown in the figure is '1' with probability 0.8 \(\big(P(X = 1) = 0.8\big)\). The cross-over probability is \(p = \frac{1}{7}\).#### Diagram Explanation:- The diagram represents the possible transitions between input \(X\) and output \(Y\).- If \(X = 0\): - The probability to receive \(Y = 0\) is \(1 - p\). - The probability to receive \(Y = 1\) is \(p\).- If \(X = 1\): - The probability to receive \(Y = 1\) is \(1 - p\). - The probability to receive \(Y = 0\) is \(p\).``` 1 - pX = 0 -----> Y = 0 \ ^ \ / \ p / v /X = 1 -----> Y = 1 1 - p```#### Problem Statement:If the received symbol is \(Y = 0\), what is the conditional probability that \(X = 1\) was transmitted?##### Options:- a. \(\frac{1}{5}\)- b. \(\frac{2}{5}\)- c. \(\frac{3}{5}\)- d. \(\frac{4}{5}\)*This question pertains to the understanding and computation of conditional probabilities within the context of a binary symmetric channel.*The correct answer should be determined after conducting the necessary calculations and analysis of the probabilities.

LetThe event "X=1" as AThe event "Y=0" as BThe probability of A i.e., P( A ) = 0.8P( B | A ), is the…

Answered: 15) The figure below shows a binary…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits. A. List the possible outcomes (sample space) for winning on the first roll of the dice. B. What is the probability that a player wins the game on the first roll of the dice? C. List the possible outcomes (sample space) for losing on the first roll of the dice. D. What is the probability that a player loses the game on the…
only B please

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