Probability, Random Variables, and Stochastic Processes

a₁ assume autocorrelation characteristic function coefficients coin conclude conditional density conditional entropy consists cyclostationary defined definition denote density f(x determine discrete type elementary events elements entropy equals equation error estimate event Example expected values experiment Figure filter find the probability follows Fourier Frequency interpretation function g(x given Hence independent input integral interval joint density jointly normal k₁ k₂ linear Markoff obtain orthogonal outcomes output P₁ parameter partition Poisson distributed Poisson points power spectrum problem process x(t PROOF R(t₁ random variables RVs x S₁ sequence specific staircase function stationary stationary process statistics stochastic process subsets Suppose t₁ t₂ takes the values theorem tossing transform trials uncorrelated variance white noise Wiener process x₁ y₁ yields zero mean σ²