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    • x giving a maximum entropy subject to the condition that the standard deviation of x be fixed at is Gaussian. To show this we must maximize x x log p x dx with See more

    1 4 W 2 W 4 W 2 W 0

    On expansion this leads to the equation given above for this case. 2. THE DISCRETE … See more

    Harvard Mathematics …
    p i j

    ✪ åj p i j We define the conditional entropy of y, Hx y as the average of the entropy of y for each value of x, weighted according to the probability of getting that particular x. That is… See more

    Harvard Mathematics Department
    j log pi j

    This is the entropy of the source per symbol of text. If the Markoff process is proceeding at a definite time rate there is also an entropy per second See more

    Harvard Mathematics Department
    Bi log p Bi

    where the sum is over all sequences Bi containing N symbols. Then GN is a monotonic decreasing function of N and Lim GN H N ¥ Theorem 6: Let p Bi Sj be the probabi… See more

    Harvard Mathematics Department
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  1. A Mathematical Theory of Communication - Wikipedia

  2. Claude E. Shannon: Founder of Information Theory

  3. Information technology: A digital genius at play | Nature

    Jul 13, 2017 · The US mathematician and electrical engineer Claude Shannon, whose life spanned the tumultuous, technologically explosive twentieth century, is often called the father of information theory.

  4. How Information Theory Changed the World - IEEE Xplore