This is an overview of the topics that are covered in the course:
Probability Theory: random variables, probability distributions, moments, multivariate distributions, functions of random variables, parametric estimation, maximum-likelihood estimation.
Random Processes: moments of random processes, ergodicity, the Poisson process, the Wiener process and white noise, stationarity, estimation, linear systems and random processes, power spectrum.
Optimal Filtering: minimum mean square error, parametric estimation, optimal finite-observation linear filters, Kalman filters.

The contents of the course are as follows:
I. Probability and Random Variables
a) Transformations and Operations on Random Variables
b) Vector Random Variables and Sequence of Random Variables.
c) Minimum Mean-Square Estimation, the Orthogonality Principles
d) The Multivariate Distribution.
II. Random Processes and Spectral Analysis
a) Stationary Concepts, Correlation Functions.
b) Time Averages, Ergodicity.
c) Correlation Functions and Power Spectrum of Stationary Processes.
d) Noise Mechanisms, the Gaussian and Poisson Processes.
e) Representations of Random Processes, Orthogonal Expansions.
III. Transformations and Operations on Random Processes
a) Linear Systems with Random Inputs.
b) Representation and Processing of Narrowband Random Processes.
c) Finite-State Linear Systems Driven by White Noise.
IV. Optimum Linear Systems
a) The Formulation of Optimum Systems.
b) Optimum Linear Systems that Maximize Signal-to-Noise Ratio.
c) The Orthogonality Principles in Linear Mean-Square Estimation.
d) Least Mean-Square Error Filtering, Estimation, Prediction, and the Wiener Filter Theory.