A maximally mixed state, the quantum analog of the uniform probability distribution, has maximum von Neumann entropy.
2.
Indeed such uniform probability distributions have maximum possible entropy H ( X ) = \ log _ 2 ( n ).
3.
"' Truncated binary encoding "'is an entropy encoding typically used for uniform probability distributions with a finite alphabet.
4.
|3 = The th cumulant of the uniform probability distribution on the interval [ " 1, 0 ] is } }.
5.
At the other extreme, if X is the uniform probability distribution with n possible values, intuitively one would expect X is associated with the most uncertainty.
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In Bayesian statistics, Bayes'rule is often applied with a so-called improper prior, for instance, a uniform probability distribution over all real numbers.
7.
Exact t-designs over quantum states cannot be distinguished from the uniform probability distribution over all states when using t copies of a state from the probability distribution.
8.
The uniform probability distribution on the space of these bitstrings assigns exactly equal weight 2 " " n " to each string of length " n ".
9.
In some cases the value of a quantile may not be uniquely determined, as can be the case for the median ( 2-quantile ) of a uniform probability distribution on a set of even size.
10.
For a set of symbols with a uniform probability distribution and a number of members which is a power of two, Huffman coding is equivalent to simple binary block encoding, e . g ., ASCII coding.
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