write a function H(p1, p2) that determines the entropy of a four-state system, if it is known that the probability of occurrence of the 3rd and 4th events is the same. what the maximum values of this function?*photo is an example for this question Task 3. Write a function H(p1, p2) that determines the entropy of a three-statesystem. What is the maximum value of this function?Solution. Consider a system X with three states x1, x2, x3. State probabilities:X₁ X1 X2X3Pi P₁ P2 1- P1 - P2The entropy of such a system is:H (P1, P2) ==-P₁ log p₁ - p2 log p2 - (1- P1 - P2) log(1- P₁ - P2).The entropy of the system is maximum if the states of the system are equallyprobable:Xi X1 X2 X3Piand is equal to the logarithm of the number of states. Therefore, the function H(p1,p2) reaches a maximum at the point (1/3, 1/3) and the largest value of the functionis Hmax(p1, p2) = log 3.

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write a function H(p1, p2) that determines the entropy of a four-state system, if it is known that the probability of occurrence of the 3rd and 4th events is the same. what the maximum values of this function? *photo is an example for this question

write a function H(p1, p2) that determines the entropy of a four-state system, if it is known that the probability of occurrence of the 3rd and 4th events is the same. what the maximum values of this function? *photo is an example for this question

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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