Probabilities, Random Variables, and Random Processes: Digital and Analog |
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... defined as / ∞∞∞ aẞfxy ( a , ẞ ) da dß ; also denoted E ( XY ) and RxY XY The covariance coefficient , defined as ( X - X ) ( YY ) The expected value of g ( X , Y ) , defined as [ [ g ( a , ẞ ) fxy ( a , ẞ ) dadẞ ; or , if X = F ( U ...
... defined as / ∞∞∞ aẞfxy ( a , ẞ ) da dß ; also denoted E ( XY ) and RxY XY The covariance coefficient , defined as ( X - X ) ( YY ) The expected value of g ( X , Y ) , defined as [ [ g ( a , ẞ ) fxy ( a , ẞ ) dadẞ ; or , if X = F ( U ...
Page 98
... define random variables . ( a ) The variable X , defined by the rule that maps the points of S onto the real axis with a value equal to the number of the top face of the die . ( b ) The variable Y , defined by the rule that maps the ...
... define random variables . ( a ) The variable X , defined by the rule that maps the points of S onto the real axis with a value equal to the number of the top face of the die . ( b ) The variable Y , defined by the rule that maps the ...
Page 147
... defined by a rule that maps points of a sample description space onto the real axis . Three important functions were defined to facilitate answering probabilistic questions about a random variable . The cumulative distribution function ...
... defined by a rule that maps points of a sample description space onto the real axis . Three important functions were defined to facilitate answering probabilistic questions about a random variable . The cumulative distribution function ...
Contents
1 | 3 |
5 | 54 |
General Formulation and Solution of Problems | 69 |
Copyright | |
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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