Probability and Random Variables
(a) Basic Theory
(b) Transformations and Operations on Random
Variables.
(c) Vector Random Variables and Sequence of
Random Variables.
(d) Minimum Mean-Square Estimation, the
Orthogonality Principles.
(e) 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 Random Processes.
(d) Some Important Random Processes.

III. Transformations and Operations on Random
Processes.
(a) Linear Systems with Random Inputs.
(b) Representation and Processing of
Band-Limited Random Processes.
(c) Finite-State Linear Systems Driven by White
Noise.

IV. Optimum Linear Systems.
(a) Formulation of Optimum Linear Systems.
(b) Optimum Linear Systems that Maximize
Signal-to-Noise Ratio (SNR).
(c) The Orthogonality Principles in Linear
Mean-Square Estimation.
(d) Least Mean-Square Error Filtering,
Estimation, Prediction, and the Wiener Filter Theory.
(e) Basic Principle of Kalman Filtering.