For a probability density function p(x) > 0 on the interval(-∞, ∞) the entropy functional S[p] is given byS[p] = − [% da p(a) log p(x).- 5%dxSuppose that the function p(x) is subject to the constraintsSo dr p(x) = 1 andL-∞.00dx 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 byp(x) = exp(−1 – λ − µƒ(x)),--where and μ are Lagrange multipliers.

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 17E

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