Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 151
... Evaluate X , X2 , and o for the random variable of Problem 3 . ( b ) Evaluate these averages on a time average basis and state whether or not you are surprised at the results . For example on a time average basis , 1 x2 = { f2x2 ( 1 ) ...
... Evaluate X , X2 , and o for the random variable of Problem 3 . ( b ) Evaluate these averages on a time average basis and state whether or not you are surprised at the results . For example on a time average basis , 1 x2 = { f2x2 ( 1 ) ...
Page 229
... evaluate X , Y , Rxy = XY and Lxy = ( X - X ) ( YY ) . 12. For the random variables of Problem 3 evaluate X , Y , XY and ( X - X ) ( Y - Y ) 13. Reconsidering Problem 4 , let us use the fundamental theorem in two ways . - ( a ) First ...
... evaluate X , Y , Rxy = XY and Lxy = ( X - X ) ( YY ) . 12. For the random variables of Problem 3 evaluate X , Y , XY and ( X - X ) ( Y - Y ) 13. Reconsidering Problem 4 , let us use the fundamental theorem in two ways . - ( a ) First ...
Page 286
... evaluate R ( 7 ) we must consider two different ranges of T. For the range 0 < T < b , the joint mass function for X1 = x ( t ) and X , = x ( t + T ) must now be evaluated for P ( 0,0 ) , P ( 0 , 1 ) , P ( 1,0 ) , and P ( 1 , 1 ) ...
... evaluate R ( 7 ) we must consider two different ranges of T. For the range 0 < T < b , the joint mass function for X1 = x ( t ) and X , = x ( t + T ) must now be evaluated for P ( 0,0 ) , P ( 0 , 1 ) , P ( 1,0 ) , and P ( 1 , 1 ) ...
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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