This is an advanced course on probability, random variables, estimation theory, and stochastic process, and will cover
\begin{itemize}
\item \textbf{Probability and random variables:} review of the probability theory, discrete and continuous random variables,
functions and transformations of random variables, conditional and joint distributions, continuous and discrete distributions, mean, variance and higher order moments, and order statistics. 
\item \textbf{Estimation and prediction:} linear estimation, minimum mean square estimation (MMSE), parameter estimation,  Baysian estimation, and maximum-likelihood estimation.
\item \textbf{Convergence and limit theorems:} convergence in probability, convergence in mean square sense, convergence in distribution, laws of large numbers, and central limit theorem. 
\item \textbf{Random processes:} discrete-time random process,  continuous-time random process correlation,  stationary, non-stationary, and ergodic processes, independent and identically
distributed (i.i.d.) processes, Poisson process, Markov chain, random walk, Wiener process, Brownian motion, spectral analysis, Gaussian process and response of linear systems to random processes.
\end{itemize}