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1. Compare the information rate between a source generating symbols at 50 symbols per second with an entropy of 1 bit per symbol and another source generating 200 symbols per second with an entropy of 0.5 bits per symbol. 2. Calculate the entropy of rolling a fair six-sided die.A biased six-sided die has probabilities: P(1)=0.1, P(2)=0.1, P(3)-0.2, P(4)-0.2, P(5)=0.2, and P(6)=0.2. What is the entropy of this die? 3. Suppose a source generates four possible symbols with probabilities: P(A)=0.1, P(B)=0.4, P(C)=0.4, and P(D)=0.1. Calculate the entropy of this source. 4. If you have a system with three states where P(X)-0.3, P(Y)-0.5, and P(Z)-0.2, what is the entropy of the system? 5. You are given a random event with three possible outcomes: P(A)=0.5, P(B)=0.3, and P(C)=0.2. Calculate the information content for each outcome in bits. 6. A weather forecast predicts a 30% chance of rain, 60% chance of cloudy weather, and 10% chance of sunshine. What is the information content for each outcome?

1. Compare the information rate between a source generating symbols at 50 symbols per second with an entropy of 1 bit per symbol and another source generating 200 symbols per second with an entropy of 0.5 bits per symbol. 2. Calculate the entropy of rolling a fair six-sided die.A biased six-sided die has probabilities: P(1)=0.1, P(2)=0.1, P(3)-0.2, P(4)-0.2, P(5)=0.2, and P(6)=0.2. What is the entropy of this die? 3. Suppose a source generates four possible symbols with probabilities: P(A)=0.1, P(B)=0.4, P(C)=0.4, and P(D)=0.1. Calculate the entropy of this source. 4. If you have a system with three states where P(X)-0.3, P(Y)-0.5, and P(Z)-0.2, what is the entropy of the system? 5. You are given a random event with three possible outcomes: P(A)=0.5, P(B)=0.3, and P(C)=0.2. Calculate the information content for each outcome in bits. 6. A weather forecast predicts a 30% chance of rain, 60% chance of cloudy weather, and 10% chance of sunshine. What is the information content for each outcome?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1. Compare the information rate between a source generating symbols at 50 symbols per second with an entropy of 1 bit per symbol and another source generating 200 symbols per second with an entropy of 0.5 bits per symbol. 2. Calculate the entropy of rolling a fair six-sided die.A biased six-sided die has probabilities: P(1)=0.1, P(2)=0.1, P(3)-0.2, P(4)-0.2, P(5)=0.2, and P(6)=0.2. What is the entropy of this die? 3. Suppose a source generates four possible symbols with probabilities: P(A)=0.1, P(B)=0.4, P(C)=0.4, and P(D)=0.1. Calculate the entropy of this source. 4. If you have a system with three states where P(X)-0.3, P(Y)-0.5, and P(Z)-0.2, what is the entropy of the system? 5. You are given a random event with three possible outcomes: P(A)=0.5, P(B)=0.3, and P(C)=0.2. Calculate the information content for each outcome in bits. 6. A weather forecast predicts a 30% chance of rain, 60% chance of cloudy weather, and 10% chance of sunshine. What is the information content for each outcome?
Transcribed Image Text:1. Compare the information rate between a source generating symbols at 50 symbols per second with an entropy of 1 bit per symbol and another source generating 200 symbols per second with an entropy of 0.5 bits per symbol. 2. Calculate the entropy of rolling a fair six-sided die.A biased six-sided die has probabilities: P(1)=0.1, P(2)=0.1, P(3)-0.2, P(4)-0.2, P(5)=0.2, and P(6)=0.2. What is the entropy of this die? 3. Suppose a source generates four possible symbols with probabilities: P(A)=0.1, P(B)=0.4, P(C)=0.4, and P(D)=0.1. Calculate the entropy of this source. 4. If you have a system with three states where P(X)-0.3, P(Y)-0.5, and P(Z)-0.2, what is the entropy of the system? 5. You are given a random event with three possible outcomes: P(A)=0.5, P(B)=0.3, and P(C)=0.2. Calculate the information content for each outcome in bits. 6. A weather forecast predicts a 30% chance of rain, 60% chance of cloudy weather, and 10% chance of sunshine. What is the information content for each outcome?
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