Pate: //20 A rondom Variable x takes value X; with Bobab 2 Pi with i=1N labelling all possibilities. The Value of x is given.
Pate: //20 A rondom Variable x takes value X; with Bobab 2 Pi with i=1N labelling all possibilities. The Value of x is given.
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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Pate: / /20
A rondom Variable x takes value X; with Bobabilty
Xi
i = 1,..., labelling all possibilities. The mean
Pi, with
N
value of x is given,
N
X = 1/ // Pixi
Ni=1
is
And, Shonon entropy of x
given as,
N
S(X) == // PilogPi
•)-Find the
distribution
the distribution which maximises Shonon
entropy. Formulate this as Longronge multiplier problem
and solve it to find relevant distribution?
b)-Find distribution which
(Note: Values Xi are considered to be fixed.).
maximises the Shonon entropy
for a fixed value of meon X. Formulate this as
a Longronge multiplier problem and show that
which ever it has forme
d
the distribution which solves
Pi = 1 = PX ₁
Z
where, B and Z
not
in principle (but may be
in practise) be found in terms of values
Con
{X; } . X and N-
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