Deterministic signals and linear time-invariant systems are studied. The Fourier transform is introduced, and its properties are reviewed. The concepts of probability and random variables are developed. Conditional probability is defined, and the total probability theorem and Bayes’ rule are given. Random variables are studied through their cumulative distribution functions and probability density functions, and statistical averages, including the mean and variance, are defined. These concepts are extended to random vectors. In addition, the concept of random processes is covered in depth. The autocorrelation function, stationarity, and power spectral density are studied, along with extensions to multiple random processes. Particular attention is paid to wide-sense stationary processes, and the concept of power spectral density is introduced. Also explored is the filtering of wide-sense stationary random processes, including the essential properties of their autocorrelation function and power spectral density. Due to their significance in modeling noise in a communication system, Gaussian random processes are also covered.