Probabilities, random variables, and random processes:

assumed autocorrelation function average axiom balls Chapter Consider the random convolution correlation integrals cross-correlation cross-correlation function cumulative distribution function defined definition delta function denoted derivation deterministic discrete Fourier transform discrete probability theory discrete random process discrete random variables DRILL SET ensemble ergodic evaluate event space Example first-order stationary formula fundamental theorem fxY(a,P given impulse response joint density function joint mass function Laplace transform Laurent series linear system mean square value member waveform mutually exclusive notation obtained otherwise periodic function periodic waveform permutations plotted in Figure points power spectral density probability measure problem properties pulse px(a random input random phenomenon range Rxx(k Rxx(r Rxx(t Rxy(r sample description space sampled values second-order stationary set theory shown in Figure shown plotted signal sketch SOLUTION solved stationary random process statistics Sxx(u Ticket Pays two-sided Laplace transform two-sided z transform typical member variance Wiener filter zero-mean