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A rondom Variable x takes value X; with Robabilty Pi, with (= 1,... N labelling all possibilities. The meats value of x is given, I cl N X = = = = = = Pixi i=1

A rondom Variable x takes value X; with Robabilty Pi, with (= 1,... N labelling all possibilities. The meats value of x is given, I cl N X = = = = = = Pixi i=1

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Day Tate:. /20 A rondom Variable x takes value X; with Probabilty Pi with i=1 labelling all possibilities. The mean Value of x is given, N X = 1 ≤ Pixi Ni=1 And Shamon entropy of x is given as N S(x)= & PilogPi (= 1 Find the distribution which maximises Shonon entropy. Formulate this as Longsonge multiplier problem and solve it to find relevant distribution? (Note: Values Xi are considered to be fixed.). b)-Find distribution which maximises the Shonon entropy for a fixed value of meon X Formulate this as a Longsonge multiplier problem and show that the distribution which solver it has form, d 1PXi in principle (but may be in practive) be found in terms of values Pi where, B and Z not = Z Con {X₁3X and N-
Transcribed Image Text:Day Tate:. /20 A rondom Variable x takes value X; with Probabilty Pi with i=1 labelling all possibilities. The mean Value of x is given, N X = 1 ≤ Pixi Ni=1 And Shamon entropy of x is given as N S(x)= & PilogPi (= 1 Find the distribution which maximises Shonon entropy. Formulate this as Longsonge multiplier problem and solve it to find relevant distribution? (Note: Values Xi are considered to be fixed.). b)-Find distribution which maximises the Shonon entropy for a fixed value of meon X Formulate this as a Longsonge multiplier problem and show that the distribution which solver it has form, d 1PXi in principle (but may be in practive) be found in terms of values Pi where, B and Z not = Z Con {X₁3X and N-
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