The differential entropy of a continuous random variable x, Project Management

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The differential entropy of a continuous random variable x

The differential entropy of a continuous random variable X is defined by the integral of (5.66). Similarly, the differential entropy of a continuous random vector X is defined by the integral of (5.68). These two integrals may not exist. Justify this statement.

Show that the differential entropy of a continuous random variable X is invariant to translation; that is

for some constant c.

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