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Results tagged with entropy
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user 276940
A mathematical quantity designed to measure the amount of randomness of a random variable.
7
votes
Proving that Shannon entropy is maximised for the uniform distribution
1 \tag{2}$$
Substituting equation (1) into equation (2):
$$\sum_i^k e^{-(1+\lambda)} = 1 \implies$$
$$k e^{-(1+\lambda)} = 1 $$
Since $p_i = e^{-(1+\lambda)}$
$$p_i = \frac{1}{k}$$
The Shannon Entropy …
- 151
2
votes
Accepted
Shannon Information | Understanding from a Microstate Perspective
$H(X) = \log_2 2 = 1 \;\mathrm{bits}$
For the biased coin where heads has a probability $p_h = 0.3$ the entropy is,
$$H(X) = - ( 0.3 \log_2 0.3 + 0.7 \log_2 0.7) = 0.88\;\mathrm{bits}$$
The entropy for … In my opinion the best and most clear understanding of entropy is "Where We Do Stand on Maximum Entropy"[pg. 12-27] by E.T. Jaynes …
- 151
1
vote
Accepted
"Entropy" in Fantasy Football League
League A does have more entropy.
In the Boltzmann equation for entropy:
$$S=k \ln W$$
$W$ is defined as the "ways" or complete set of possible configurations of a system. … In a Maximum Entropy sense, because this is an unconstrained problem and have no more information, this problem would match the Laplace "Principle of Indifference" which simplifies into the uniform distribution …
- 151
1
vote
Conflicting Definition of Information in Statistics | Fisher Vs Shannon
The higher entropy at $P(X = 0.5)$ produces the maximum uncertainty. …
- 151