Chapter 1 Mathematical Background
Lecture 1.1 Infinite Series (Video) (Slide)
Lecture 1.2 Approximation (Video) (Slide)
Lecture 1.3 Integration (Video) (Slide)
Lecture 1.4 Linear Algebra (Video) (Slide)
Lecture 1.5 Combinatorics (Video) (Slide)
Chapter 2 Probability
Lecture 2.1 Set Theory (Video) (Slide)
Lecture 2.2 Probability Space (Video) (Slide)
Lecture 2.3 Axioms of Probability (Video) (Slide)
Lecture 2.4 Conditional Probability (Video) (Slide)
Lecture 2.5 Independence (Video) (Slide)
Lecture 2.6 Bayes Theorem (Video) (Slide)
Chapter 3 Discrete Random Variables
Lecture 3.1 Random Variables(Video) (Slide)
Lecture 3.2 Probability Mass Function (Video) (Slide)
Lecture 3.3 Cumulative Distribution Function (Video) (Slide)
Lecture 3.4 Expectation (Video) (Slide)
Lecture 3.5 Moments and variance (Video) (Slide)
Lecture 3.6 Bernoulli random variables (Video) (Slide)
Lecture 3.7 Binomial random variables (Video) (Slide)
Lecture 3.8 Geometric random variables (Video) (Slide)
Lecture 3.9 Poisson random variables (Video) (Slide)
Chapter 4 Continuous Random Variables
Lecture 4.1 Probability density function (Video) (Slide)
Lecture 4.2 Expectation (continuous) (Video) (Slide)
Lecture 4.3 Cumulative distribution function (continuous) (Video) (Slide)
Lecture 4.4 Mean, mode, median (Video) (Slide)
Lecture 4.5 Uniform random variables (Video) (Slide)
Lecture 4.6 Exponential random variables (Video) (Slide)
Lecture 4.7 Gaussian random variables (Video) (Slide)
Lecture 4.8 Transformation of random variables (Video) (Slide)
Lecture 4.9 Generating random numbers (Video) (Slide)
Chapter 5 Joint Distributions
Lecture 5.1 Joint PMF, PDF, and CDF (Video) (Slide)
Lecture 5.2 Joint expectation (Video) (Slide)
Lecture 5.3 Correlation and covariance (Video) (Slide)
Lecture 5.4 Conditional distributions (Video) (Slide)
Lecture 5.5 Conditional expectation (Video) (Slide)
Lecture 5.6 Sum of two random variables (Video) (Slide)
Lecture 5.7 Examples for sum of two random variables (Video) (Slide)
Lecture 5.8 Random vector and covariance matrix (Video) (Slide)
Lecture 5.9 Multi-dimensional Gaussian (Video) (Slide)
Lecture 5.10 Gaussian whitening (Video) (Slide)
Lecture 5.11 Principal component analysis (Video) (Slide)
Chapter 6 Sample Statistics
Lecture 6.1 Moment generating functions (Video) (Slide)
Lecture 6.2 Characteristic functions (Video) (Slide)
Lecture 6.3 Jensen's inequality (Slide)
Lecture 6.4 Markov and Chebyshev inequality (Slide)
Lecture 6.5 Law of Large Numbers (Slide)
Lecture 6.6 Central Limit Theorem (Slide)
Chapter 8 Estimation
Lecture 8.1 Maximum Likelihood Estimation (Slide)
Lecture 8.2 Properties of ML Estimators (Slide)
Lecture 8.3 Maximum a Posteriori Estimation (Slide)
Lecture 8.4 Minimum Mean Square Estimation (Slide)
Chapter 10 Random Processes
Lecture 10.1 Intro to random processes (Video) (Slide)
Lecture 10.2 Mean functions (Video) (Slide)
Lecture 10.3 Autocorrelation functions (Video) (Slide)
Lecture 10.4 Autocovariance functions, independent processes (Video) (Slide)
Lecture 10.5 Wide sense stationary processes (Video) (Slide)
Lecture 10.6 Power spectral density (Video) (Slide)
Lecture 10.7 Linear time invariant systems (Video) (Slide)
Lecture 10.8 Mean and autocorrelation through LTI systems (Video) (Slide)
Lecture 10.9 Cross-correlation through LTI systems (Video) (Slide)