For a probability density function p(x) > 0 on the interval (-∞, ∞) the entropy functional S[p] is given by S[p] = − [% da p(a) log p(x). - 5% dx Suppose that the function p(x) is subject to the constraints So dr p(x) = 1 and L -∞ .00 dx f(x)p(x) = c, where f(x) is a fixed function and c is a constant. Show that is a stationary path for S[p] is given by p(x) = exp(−1 – λ − µƒ(x)), - - where and μ are Lagrange multipliers.
For a probability density function p(x) > 0 on the interval (-∞, ∞) the entropy functional S[p] is given by S[p] = − [% da p(a) log p(x). - 5% dx Suppose that the function p(x) is subject to the constraints So dr p(x) = 1 and L -∞ .00 dx f(x)p(x) = c, where f(x) is a fixed function and c is a constant. Show that is a stationary path for S[p] is given by p(x) = exp(−1 – λ − µƒ(x)), - - where and μ are Lagrange multipliers.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![For a probability density function p(x) > 0 on the interval
(-∞, ∞) the entropy functional S[p] is given by
S[p] = − [% da p(a) log p(x).
- 5%
dx
Suppose that the function p(x) is subject to the constraints
So dr p(x) = 1 and
L
-∞
.00
dx f(x)p(x) = c,
where f(x) is a fixed function and c is a constant.
Show that is a stationary path for S[p] is given by
p(x) = exp(−1 – λ − µƒ(x)),
-
-
where and μ are Lagrange multipliers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2Fe65dc56c-5a63-4cae-8a32-3cb1c9627427%2Fwvucuwq_processed.png&w=3840&q=75)
Transcribed Image Text:For a probability density function p(x) > 0 on the interval
(-∞, ∞) the entropy functional S[p] is given by
S[p] = − [% da p(a) log p(x).
- 5%
dx
Suppose that the function p(x) is subject to the constraints
So dr p(x) = 1 and
L
-∞
.00
dx f(x)p(x) = c,
where f(x) is a fixed function and c is a constant.
Show that is a stationary path for S[p] is given by
p(x) = exp(−1 – λ − µƒ(x)),
-
-
where and μ are Lagrange multipliers.
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