Probability, Random Variables, and Random Signal PrinciplesThere are now 134 examples and nearly 900 homework problems; and other topics expanded or added include discussion of probability as a relative frequency, permutations, combinations, transformations of random variables, ergodicity of random processes, laws of large numbers, estimation, various inequalities, properties of impulses, and chapter-end summaries. This new material will prove most useful for students concerned with modern digital systems."--BOOK JACKET. |
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Page 152
... covariance matrix of the N random variables , are given by Signal Principles i = j - C¡¡ = E [ ( X ; — X¡ ) ( X ; — X ; ) ] - { 0 } ; = Pcx ( 5.3-15 ) CX , Xi i #j The density ( 5.3-12 ) is often called the N - variate gaussian density ...
... covariance matrix of the N random variables , are given by Signal Principles i = j - C¡¡ = E [ ( X ; — X¡ ) ( X ; — X ; ) ] - { 0 } ; = Pcx ( 5.3-15 ) CX , Xi i #j The density ( 5.3-12 ) is often called the N - variate gaussian density ...
Page 177
... covariance matrix 4 2.05 1.05 [ Cx ] = 2.05 4 2.05 177 CHAPTER 5 : Operations on Multiple Random Variables 1.05 2.05 4 are transformed to new variables Y1 = 5X1 + 2X2 – X3 Y2 = −X1 + 3X2 + X3 - Y3 = 2X1 = X2 + 2X3 ( a ) Find the covariance ...
... covariance matrix 4 2.05 1.05 [ Cx ] = 2.05 4 2.05 177 CHAPTER 5 : Operations on Multiple Random Variables 1.05 2.05 4 are transformed to new variables Y1 = 5X1 + 2X2 – X3 Y2 = −X1 + 3X2 + X3 - Y3 = 2X1 = X2 + 2X3 ( a ) Find the covariance ...
Page 454
... Covariance : of independent random variables , 145 of orthogonal random variables , 145 of random variables , 144 , 168 of uncorrelated random variables , 145 , 168 Covariance functions ( See Correlation functions ) Covariance matrix ...
... Covariance : of independent random variables , 145 of orthogonal random variables , 145 of random variables , 144 , 168 of uncorrelated random variables , 145 , 168 Covariance functions ( See Correlation functions ) Covariance matrix ...
Contents
Venn Diagram Equality and Difference Union | 7 |
Joint Probability Conditional Probability Total | 18 |
The Random Variable | 107 |
Copyright | |
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Probability, Random Variables, and Random Signal Principles Peyton Z. Peebles No preview available - 2001 |
Common terms and phrases
amplitude applied assume autocorrelation function available power gain average power band-limited bandpass bandwidth CHAPTER characteristic function cos(wpt covariance cross-correlation cross-correlation function cross-power defined denoted discrete random variables discrete-time DT system ergodic event example expected value Fourier transform frequency fx(x fy(y gaussian random variables given impulse response independent random variables integral joint density function jointly wide-sense stationary k₁ Linear Systems lowpass mean value Multiple Random Variables noise figure noise power noise temperature Peebles power density spectrum power spectrum Problem properties random process random process X(t Random Signal Principles random variables X1 real constants resistor Rxy(t Ryy(t sample function sample space sequence signal x(t spectral stationary process statistically independent statistically independent random Systems with Random t₁ transfer function uncorrelated variance voltage W₁ W₂ waveform white noise wide-sense stationary X₁ xx(w Y₁ Y₂ zero zero-mean