A xondom Variable x takes value X; with Probabilty Pi, with i = 1,... N labelling all possibilities. The meon Value of X is given, And Shonon entropy of x S(x) = H1 N i=1 is it It N ≤ Pixi - given as, Z PilogPi i=1 chu

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Chapter1: Combinatorial Analysis
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Jay: -
Pate: /20
A random Variable x takes value X; with Probabilty
Pi with i=1,N labelling all possibilities. The mean
Value of X is given,
N
< Pixi
X = = = = = = = = 1
1
i=1
And Shonon entropy of X is
is given as,
Pilog Pi
N
S(x)=
1
Find the distribution which maximises Shonon
entropy-Formulate this as Longsonge multiplier problem
and solve it to find relevant distribution?
(Note: Values Xi ase considered to be fixed.)
Transcribed Image Text:Jay: - Pate: /20 A random Variable x takes value X; with Probabilty Pi with i=1,N labelling all possibilities. The mean Value of X is given, N < Pixi X = = = = = = = = 1 1 i=1 And Shonon entropy of X is is given as, Pilog Pi N S(x)= 1 Find the distribution which maximises Shonon entropy-Formulate this as Longsonge multiplier problem and solve it to find relevant distribution? (Note: Values Xi ase considered to be fixed.)
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