For a continuous random variable (X) with distribution (p_{X}(x)), the uncertainty is measured by the so-called differential

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For a continuous random variable $X$ with distribution $p_{X}(x)$, the uncertainty is measured by the so-called differential entropy $h(X)$ determined as (Cover \& Thomas, 2006)

\[H(X)=-\int_{x} p_{X}(x) \log _{b} p_{X}(x) \mathrm{d} x .\]

Determine the differential entropy of the random variables characterized by:

(a) continuous uniform distribution $u_{X, \mathrm{c}}(x)$ given in Equation (1.207)

(b) the Gaussian distribution $\phi_{X}(x)$ given in Equation (1.209).

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Digital Signal Processing System Analysis And Design

ISBN: 9780521887755

2nd Edition

Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto

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Question Posted: Mar 27, 2024 02:01 AM

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For a continuous random variable (X) with distribution (p_{X}(x)), the uncertainty is measured by the so-called differential

Question:

1 ox(x) = e-(x-)/22 2x02 (1.209)

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Digital Signal Processing System Analysis And Design

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