Probabilistic System Analysis and Applied Probability (Fall 2010) (M-I-T)

• Lecture 1 Probability Models and Axioms
• Lecture 2 Conditioning and Bayes’ Rule
• Lecture 3 Independence
• Lecture 4 Counting
• Lecture 5 Discrete Random Variables; Probability Mass Functions; Expectations
• Lecture 6 Discrete Random Variable Examples; Joint PMFs
• Lecture 7 Multiple Discrete Random Variables Expectations, Conditioning, Independence
• Lecture 8 Continuous Random Variables
• Lecture 9 Multiple Continuous Random Variables
• Lecture 10 Continuous Bayes’ Rule; Derived Distributions
• Lecture 11 Derived Distributions; Convolution; Covariance and Correlation
• Lecture 12 Iterated Expectations; Sum of a Random Number of Random Variables
• Lecture 13 Bernoulli Process
• Lecture 14 Poisson Process I
• Lecture 15 Poisson Process II
• Lecture 16 Markov Chains I
• Lecture 17 Markov Chains II
• Lecture 18 Markov Chains III
• Lecture 19 Weak Law of Large Numbers
• Lecture 20 Central Limit Theorem
• Lecture 21 Bayesian Statistical Inference I
• Lecture 22 Bayesian Statistical Inference II
• Lecture 23 Classical Statistical Inference I
• Lecture 24 Classical Inference II