By John R. Pierce
Covers encoding and binary digits, entropy, language and that means, effective encoding and the noisy channel, and explores ways that info conception pertains to physics, cybernetics, psychology, and artwork. "Uncommonly good...the such a lot pleasing dialogue to be found." - clinical American. 1980 version.
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This joint ensemble has the special property that its two marginal distributions, P (x) and P (y), are identical. 1. 3). The probability P (y | x = q) is the probability distribution of the second letter given that the first letter is a q. 3. Conditional probability distributions. (a) P (y | x): Each row shows the conditional distribution of the second letter, y, given the first letter, x, in a bigram xy. (b) P (x | y): Each column shows the conditional distribution of the first letter, x, given the second letter, y.
24). No, they are not independent. f. 3). 27). We define the fraction fB ≡ B/K. (a) The number of black balls has a binomial distribution. P (nB | fB , N ) = N f nB (1 − fB )N −nB . 58) var[nB ] = N fB (1 − fB ). 1). The standard deviation of nB is var[nB ] = N fB (1 − fB ). When B/K = 1/5 and N = 5, the expectation and variance of nB are 1 and 4/5. 89. When B/K = 1/5 and N = 400, the expectation and variance of nB are 80 and 64. The standard deviation is 8. 27). 59), which is by definition the expectation of the numerator.
0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 This matrix is ‘redundant’ in the sense that the space spanned by its rows is only three-dimensional, not seven. This matrix is also a cyclic matrix. Every row is a cyclic permutation of the top row. Cyclic codes: if there is an ordering of the bits t1 . . tN such that a linear code has a cyclic parity-check matrix, then the code is called a cyclic code. The codewords of such a code also have cyclic properties: any cyclic permutation of a codeword is a codeword.