Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 112
... PROPERTIES AND USES OF DISTRIBUTION , DENSITY , AND MASS FUNCTIONS Examples 4.2 through 4.5 showed the derivation of the cumulative distri- bution function Fx ( a ) , the density function fx ( a ) , and for the case of a discrete random ...
... PROPERTIES AND USES OF DISTRIBUTION , DENSITY , AND MASS FUNCTIONS Examples 4.2 through 4.5 showed the derivation of the cumulative distri- bution function Fx ( a ) , the density function fx ( a ) , and for the case of a discrete random ...
Page 113
... properties of Fy ( a ) , it follows that the density function f ( a ) , which is defined as ( d / da ) Fx ( a ) , must possess the follow- ing two properties : 1. fx ( a ) ≥0 , since Fx ( a ) is nondecreasing . 2. √∞∞fx ( a ) da = 1 ...
... properties of Fy ( a ) , it follows that the density function f ( a ) , which is defined as ( d / da ) Fx ( a ) , must possess the follow- ing two properties : 1. fx ( a ) ≥0 , since Fx ( a ) is nondecreasing . 2. √∞∞fx ( a ) da = 1 ...
Page 175
... PROPERTIES AND USAGE OF JOINT DISTRIBUTION , DENSITY , AND MASS FUNCTIONS This section will enumerate the properties of Fxy ( α , ß ) , fxy ( α , ß ) , and Pxy ( α , B ) and then culminate in solving some probabilistic questions while ...
... PROPERTIES AND USAGE OF JOINT DISTRIBUTION , DENSITY , AND MASS FUNCTIONS This section will enumerate the properties of Fxy ( α , ß ) , fxy ( α , ß ) , and Pxy ( α , B ) and then culminate in solving some probabilistic questions while ...
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1 | 3 |
5 | 54 |
General Formulation and Solution of Problems | 69 |
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Common terms and phrases
A₁ autocorrelation function average axiom B₁ balls Chapter convolution correlation integrals cross-correlation cross-correlation function cumulative distribution function dadß defined definition delta function denoted derivation deterministic discrete Fourier transform discrete probability theory discrete random process DRILL SET ensemble ergodic evaluate event space Example finite first-order stationary formula fundamental theorem fxy(a fy(B fz(y given impulse response joint density function joint mass function Laplace transform linear system M₁ member waveform notation obtained otherwise output periodic function periodic waveform permutations plotted in Figure points power spectral density probability measure probability theory problem properties pulse px(a random input random phenomenon range Rxx(T sample description space sampled values second-order stationary set theory shown in Figure shown plotted signal sketch SOLUTION solved statistics Sxx(w Ticket Pays two-sided Laplace transform two-sided z transform typical member X₁ z transform zero-mean