Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 155
... JOINT DISTRIBUTION , DENSITY , AND MASS FUNCTIONS Two random variables defined on a sample description or event space are characterized by their joint distribution function Fxy ( a , B ) which is defined as Fxy ( α , B ) = P [ ( X ≤a ) ...
... JOINT DISTRIBUTION , DENSITY , AND MASS FUNCTIONS Two random variables defined on a sample description or event space are characterized by their joint distribution function Fxy ( a , B ) which is defined as Fxy ( α , B ) = P [ ( X ≤a ) ...
Page 171
... density functions of one random variable may be utilized to find the joint density function fxy ( α , ẞ ) as fx ( a ) fy [ B / ( X = a ) ] . In general this is much quicker to find than the joint cumulative distribution function as the ...
... density functions of one random variable may be utilized to find the joint density function fxy ( α , ẞ ) as fx ( a ) fy [ B / ( X = a ) ] . In general this is much quicker to find than the joint cumulative distribution function as the ...
Page 274
... joint density function of the random variables . For example , x ( t ) = A cos ( wt + 6 ) where A and are random variables with a joint density function ƒ1 ( α , ß ) = 1 / 4π ; 8 < a < 10 , 0 < B≤2π , designates a set of sinusoidal ...
... joint density function of the random variables . For example , x ( t ) = A cos ( wt + 6 ) where A and are random variables with a joint density function ƒ1 ( α , ß ) = 1 / 4π ; 8 < a < 10 , 0 < B≤2π , designates a set of sinusoidal ...
Contents
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5 | 54 |
General Formulation and Solution of Problems | 69 |
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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