At the end of the course, the students will be able to: 
\begin{itemize}  
\item Understand the basic principles of probability, probability axioms, independence, conditional probability, Bayes theorem and use these principles in solving problems.
\item  Characterize probability distributions of different functions of random variables and find their expected value, variance, and moments.
\item  Explain the difference between deterministic and stochastic signals providing examples in the context of signal processing and communications.
\item  Understand and reflect on the implications of the laws of large numbers and the central limit theorem in the context of signal acquisition and analysis.
%\item  Characterize random signals by computing first and second order statistics.
%\item  Calculate the bias and variance of an estimator, given the noise statistics.
\item  Apply the linear, maximum likelihood and Bayesian estimations methods to solve problems concerning the estimation of signal parameters.
%\item  Apply numerical solution methods to obtain the least squares and maximum likelihood estimates for problems with nonlinear signal models.
\item Understand and explain the use of Markov chains and process  in signal processing, communication and machine learning.
\end{itemize}