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  • probability theory - Shannon Entropy - Binary Variable - Mathematics . . .
    For a binary random variable, entropy is indeed always $\le 1$ (prove this) The point is that you can do better than 1 bit (at least if you aggregate data) E g , suppose you store the snow-or-not data for $100$ days together, where each day can be modeled independently with probablity of snowing $0 3$ Then you'd need to store roughly $100 H (0 7, 0 3) \approx 88$ bits instead of $100$
  • Shannon entropy of a fair dice - Mathematics Stack Exchange
    To recover entropy, you have to consider a sequence of dice throws, and ask how many questions per roll you need in an optimal strategy, in the limit that the number of rolls goes to infinity Note that each question can cover all the rolls, for example for two rolls, you could ask at some point: “Are the results in $\ {16,21,22,23\}$?” (where the first digit denotes the first throw, and
  • Solved 2. (10 points) Recall our table for the Restaurant - Chegg
    To approach the "Hungry" attribute, compute the entropy of the target variable "Will wait" by considering when "Hungry" is true and when "Hungry" is false
  • Solved Problem 111 (BP111). The Shannon for- mula for - Chegg
    The Shannon for- mula for entropy is (with Pi the probability of the system being in the state i) while the Boltzmann entropy is S = kB In W when the system is, in any one of a multi- plicity W of states
  • Help understanding Shannon entropy - Physics Forums
    The discussion centers around understanding Shannon entropy, its mathematical formulation, and its implications for encoding information in bits Participants explore examples from information theory, particularly focusing on how entropy relates to the average number of bits required to describe outcomes of random variables One participant expresses confusion about the connection between
  • Shannon Entropy vs Entropy in chemistry - Physics Forums
    The discussion centers on the comparison between Shannon entropy, commonly used in information theory and programming, and the concept of entropy in chemistry and physics
  • Intuitive explanation of entropy - Mathematics Stack Exchange
    I just want to point out that there are simple pieces of software around on the Internet claiming to determine (and in fact they do correctly compute according to the formula of Shannon) the "entropy" of a user-given character sequence However, entropy is a concept relevant to the source of randomness, not to a particular "given" sequence Hence such calculations are problematical See the
  • Solved (a) Suppose we have a two state system with a density - Chegg
    Show that the Shannon entropy is exponentially small, and give an intuitive interpretation for this Show that all of the Rényi entropies are equal at leading order and exponentially small (c) Now consider a density matrix p= (10) Notice that this is Hermitian and normalized to tr (e) = 1 Show that this is a pure state
  • Boltzmann Entropy Formula – Derivation • Physics Forums
    Boltzmann entropy definition is given by: S = k B l n W where W is the weight of the configuration which has the maximum number of microstates This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy However, I can't find the derivation of this equation or where does it come from Do you know a source?
  • Correct algorithm for Shannon entropy with R
    Correct algorithm for Shannon entropy with R Ask Question Asked 12 years, 3 months ago Modified 12 years, 3 months ago





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