Question: A one-dimensional normal distribution of zero mean and standard deviation is given by p(x) = (2702)-1/2 exp(-23). 202 - < x < 0. (Problem 9.1)

A one-dimensional normal distribution of zero mean and standard deviation is given

by

p(x) = (2702)-1/2 exp(-23). 202 -< x < 0.

(Problem 9.1)

(i) Show that its entropy is, where e is the base of the natural logarithms.

(ii) Show that for given

02 = [_dx xp(x)

(Problem 9.2)

the normalised probability distribution having the largest entropy is the one-dimensional normal distribution.

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