Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 5
... theory in the first three chapters . The present chapter will be devoted to the prerequisite mathematical background for discrete probability theory — that is , set theory ... THEORY 5 Review of Set Theory and Event Theory Random Phenomena.
... theory in the first three chapters . The present chapter will be devoted to the prerequisite mathematical background for discrete probability theory — that is , set theory ... THEORY 5 Review of Set Theory and Event Theory Random Phenomena.
Page 7
... set are also referred to as members or points and we will use the three terms “ element , " " point , ” and “ member " interchangeably . THE ALGEBRA OF SETS The important operation definitions used in set theory will now be enu- merated : ...
... set are also referred to as members or points and we will use the three terms “ element , " " point , ” and “ member " interchangeably . THE ALGEBRA OF SETS The important operation definitions used in set theory will now be enu- merated : ...
Page 12
... Set theory and event theory will be utilized for two of the three stages in the solution of probabilistic questions concerning a random phenomenon . In stage 1 set theory is utilized to represent the mutually exclusive , collec- tively ...
... Set theory and event theory will be utilized for two of the three stages in the solution of probabilistic questions concerning a random phenomenon . In stage 1 set theory is utilized to represent the mutually exclusive , collec- tively ...
Contents
1 | 3 |
5 | 54 |
General Formulation and Solution of Problems | 69 |
Copyright | |
12 other sections not shown
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