Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 13
... notation will be used throughout : n ! = n ( n - 1 ) x ( n − 2 ) × ... × 3 × 2 × 1 ( 1.6 ) n ! is called “ n ... notations MP , and " C , are sometimes used in place of ( M ) , and ( " ) , respectively . This is done where MP , results ...
... notation will be used throughout : n ! = n ( n - 1 ) x ( n − 2 ) × ... × 3 × 2 × 1 ( 1.6 ) n ! is called “ n ... notations MP , and " C , are sometimes used in place of ( M ) , and ( " ) , respectively . This is done where MP , results ...
Page 123
... notation . 00 o } = ƒ ° ( a− x ) 2ƒx ( a ) da -8 = ƒ °° a2ƒx ( a ) da− ƒ °° 2aXƒx ( a ) da + s ° X2ƒx ( a ) da -8 1- ∞ -∞ x2 −2X ƒ °° aƒx ( a ) da + X2ƒ °° _fx ( a ) da = X 88 ∞ = x2 -2X · X + 2.1 ( since the area of any density ...
... notation . 00 o } = ƒ ° ( a− x ) 2ƒx ( a ) da -8 = ƒ °° a2ƒx ( a ) da− ƒ °° 2aXƒx ( a ) da + s ° X2ƒx ( a ) da -8 1- ∞ -∞ x2 −2X ƒ °° aƒx ( a ) da + X2ƒ °° _fx ( a ) da = X 88 ∞ = x2 -2X · X + 2.1 ( since the area of any density ...
Page 247
... notation . Example 6.3 Prove that the random process of Example 6.2 , x ( t ) = 8 + A , where ƒ1 ( a ) = 1 ; 0 < a < 1 , is ( a ) First - order stationary . ( b ) Second - order stationary . Table 6.1 A SUMMARY OF SOME NOTATION USED FOR ...
... notation . Example 6.3 Prove that the random process of Example 6.2 , x ( t ) = 8 + A , where ƒ1 ( a ) = 1 ; 0 < a < 1 , is ( a ) First - order stationary . ( b ) Second - order stationary . Table 6.1 A SUMMARY OF SOME NOTATION USED FOR ...
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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