Upon successful completion of the course, students will be able to:

• Recall and apply probability concepts, random variables, and convergence of sequences of random variables. 

• Model and analyze real-world systems using Poisson processes.

• Characterize Gaussian random vectors and processes; compute correlations, covariances, and power spectra.

• Formulate problems as finite- and countable-state Markov chains, determine stationary distributions, and analyze long-term behavior.

• Understand renewal theory and apply it to stochastic models with repeated random events.

• Apply martingale properties and random walk models to analyze stochastic behavior in time-evolving systems.

• Employ least mean square error (LMSE) estimation and orthogonal expansions for prediction and filtering in stochastic systems.

• Develop mathematical maturity and analytical skills in applying theory to novel problems.