{"id":252332,"date":"2026-07-13T01:58:07","date_gmt":"2026-07-12T22:58:07","guid":{"rendered":"https:\/\/1kitap1.com\/en\/an-introduction-to-information-theory-fazlollah-m-reza\/"},"modified":"2026-07-13T01:58:07","modified_gmt":"2026-07-12T22:58:07","slug":"an-introduction-to-information-theory-fazlollah-m-reza","status":"publish","type":"post","link":"https:\/\/1kitap1.com\/en\/an-introduction-to-information-theory-fazlollah-m-reza\/","title":{"rendered":"An Introduction To Information Theory – Fazlollah M Reza"},"content":{"rendered":"
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1 \/ 2 ax exp – 9(‘ C \u2014 a)2 + exp \u2014 ^ ( \u2014 X \u2014 a)2 p(y) = 2 \\\/2-iray exp y \u2014 \u2014 a a + exp y \u2014 \u2014 a a y > 0 Multidimensional Case. Let (Xi,X2, . . . ,Xn) be an n-dimensional random variable with CDF F(xi,x2, . . .<\/p>\n

,xn). Let yi \u2014 ffi(Xi,x2, . . . ,x\u201e) F2 = g2(Xi,X2, . . . ,X\u201e) Yn = ?n(XX,X2, . . . ,Xn) (5-74) It can be shown without difficulty that a generalization of the rela\u00ac tion (5-73) is valid under certain appropriate circumstances. First of all, the transformation of Eqs. (5-74) must be one-to-one, and all the gic must be differentiable and have continuous Furthermore, dY, 3Fj dYi dX1 ax2 ax\u201e <9F2 ar2 au2 dXi ax2 ax\u201e 6Yn dYn 9Yn dXx ax2 dXn 5* 0 (5-75) In the second place, the variable (Xi,X2, .<\/p>\n

. . ,Xn) must possess a density function\/(xi,x2, . . . ,x\u201e). Under such assumptions, the density function of (Fi,F2, . . . , F\u201e) can be derived as a logical extension of Eqs. (5-73). pQ\/i,i\/2, \u25a0 \u2022 – ,Vn) = j^f(xi,x2, . . . ,xn) (5-76) Example 6-11. Let the density function for the random variable (X\\,X2) be Find the density function for the variable (Fi,F2), where Solution.<\/p>\n

According to Eq. (5-75), Also note that Hence. g(y 1,2\/2) The simplicity of this problem is due to the linear transformation of the variable. Otherwise, A would not remain invariant for all values of the variable. Multivalued Transformations. Let F = g(X) be any real continuous transformation defined for all possible values of the random variable X. The probability distribution for the random variable F is G(y) = P{g(X) < y} (5-77) For convenience of analysis, the range of the values of x may be divided into pieces in which y = g{x) is monotonic either nonincreasing or FlG- 5'9- ^ multivalued transformation , .<\/p>\n

TTT.,. , . of the random variable, nondecreasing. Without loss of generality, we assume that the functional relationship y \u2014 g{x) is such that in each of the above intervals y is differentiable, single-valued, and has a nonzero derivative.<\/p>\n

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This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.<\/em><\/p>\n

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