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Uncertainty in a binary source
Abstract
Entropy and normalized variance share their endpoints and maximum, but differ between them.
Definition
Binary entropy measures uncertainty in bits. It is zero at either deterministic endpoint and reaches one bit when the two outcomes are equally probable.
Normalized variance also reaches one at equal probabilities. Its shared numerical range helps compare the shapes, but does not give variance the unit “bit”.
Values calculated at equal probabilities.
Probability p
Entropy H [bit]
Variance V [1]
0.5
1
1
Interpretation
A common maximum does not make the two functions interchangeable. Definitions and units remain essential to interpreting the figure.
These values describe known theoretical functions. They do not estimate uncertainty from a measured sample or demonstrate compression performance.
HTML
<articleclass="sheet sheet-paper"lang="en"data-dd-color="grayscale"data-dd-paper="a4"> <headerclass="paper-head"><h2>Uncertainty in a binary source</h2></header> <sectionclass="abstract prose"> <h3>Abstract</h3> <p>Entropy and normalized variance share their endpoints and maximum, but differ between them.</p> </section> <divclass="paper-columns"> <sectionclass="prose"> <h3>Definition</h3> <p>Binary entropy measures uncertainty in bits. It is zero at either deterministic endpoint and reaches one bit when the two outcomes are equally probable.</p> <p>Normalized variance also reaches one at equal probabilities. Its shared numerical range helps compare the shapes, but does not give variance the unit “bit”.</p> </section> </div> <figureclass="plate plate-table plate-full"> <figcaption>Values calculated at equal probabilities.</figcaption> <divclass="table-wrap"><table> <thead><tr><th>Probability p</th><th>Entropy H [bit]</th><th>Variance V [1]</th></tr></thead> <tbody><tr><td>0.5</td><td>1</td><td>1</td></tr></tbody> </table></div> </figure> <divclass="paper-columns"> <sectionclass="prose"> <h3>Interpretation</h3> <p>A common maximum does not make the two functions interchangeable. Definitions and units remain essential to interpreting the figure.</p> <p>These values describe known theoretical functions. They do not estimate uncertainty from a measured sample or demonstrate compression performance.</p> </section> </div></article>
A paper with an abstract
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Uncertainty in a binary source
An expository typesetting specimen
Abstract
Entropy and normalized variance share their endpoints and maximum, but differ between them.
Definition
Both curves are calculated directly from their definitions.
HTML
<articleclass="sheet sheet-paper"lang="en"data-dd-color="grayscale"data-dd-paper="a4"data-dd-print-urls="sources"> <headerclass="paper-head"> <h2>Uncertainty in a binary source</h2> <pclass="paper-byline">An expository typesetting specimen</p> </header> <sectionclass="abstract prose"> <h3>Abstract</h3> <p>Entropy and normalized variance share their endpoints and maximum, but differ between them.</p> </section> <sectionclass="prose"> <h3>Definition</h3> <p>Both curves are calculated directly from their definitions.</p> </section></article>
A continuous single-column paper using the existing reading scale and shared prose and figure widths.
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