Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 104
... px ( a ) defined as Px ( a ) = P ( X = a ) is Px ( 2 ) = Px ( 12 ) = 36 Px ( 3 ) = Px ( 11 ) = 36 Px ( 4 ) = Px ( 10 ) = 3 / Px ( 5 ) = Px ( 9 ) = 3 % 4 36 Px ( 6 ) = Px ( 8 ) = 3 / 36 Px ( 7 ) = 3 % 6 36 otherwise Px ( a ) = 0 We note that ...
... px ( a ) defined as Px ( a ) = P ( X = a ) is Px ( 2 ) = Px ( 12 ) = 36 Px ( 3 ) = Px ( 11 ) = 36 Px ( 4 ) = Px ( 10 ) = 3 / Px ( 5 ) = Px ( 9 ) = 3 % 4 36 Px ( 6 ) = Px ( 8 ) = 3 / 36 Px ( 7 ) = 3 % 6 36 otherwise Px ( a ) = 0 We note that ...
Page 113
... px ( a ) The mass function px ( a ) , defined as px ( a ) = P ( X = a ) , is useful only if the random variable is discrete , which means that F ( a ) changes only with discrete jumps . By definition , it must possess the following two ...
... px ( a ) The mass function px ( a ) , defined as px ( a ) = P ( X = a ) , is useful only if the random variable is discrete , which means that F ( a ) changes only with discrete jumps . By definition , it must possess the following two ...
Page 173
... Px [ a / ( Y = 3 ) ] 0.75 0.25 2 Figure 5.4 ( a ) The joint mass function for Example 5.5 . ( b ) The required mass functions . and Px ( 1 ) = 0.4 Similarly , Px ( 2 ) = 0.3 Had we constructed an extra column in Figure 5.4a and labeled ...
... Px [ a / ( Y = 3 ) ] 0.75 0.25 2 Figure 5.4 ( a ) The joint mass function for Example 5.5 . ( b ) The required mass functions . and Px ( 1 ) = 0.4 Similarly , Px ( 2 ) = 0.3 Had we constructed an extra column in Figure 5.4a and labeled ...
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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