Lecture Slides
Session 1 Slides:
Topics: Probability Spaces, Permutations, Combinations and Conditioning
Topics: Bayes' Theorem and Counting Based Probabilty
Reading: Chapter 1.4,1.5 SR - Models and SR Prob Sections 1.2-1.5, 3.1-3.5
Problem Set: Chapter 1 - Questions 19, 25, 40, 45, 48 - SR Models. Chapter 1 - Problems 10, 11, 12, 15, 29 - SR Prob.
Topics: Random Variables, induced measure and distribution function, expectation of a random variable, computing probabilities by conditioning. Discrete distributions, Binomial, Poisson and Geometric distributions
Topics: Continuous distributions, change of variables formula, the uniform distribution and inverse transforms
Reading: SR Models Chapters 2.1-2.2, 2.4 and SR - Prob 4.1-4.7
Problem Set: SR Models Chapter 2 - Questions 4, 13, 16, 23, 27, 55(a), 55(b)
Session 5 (Couldn't upload annotated slides, as file was corrupted):
Topics: Continuous Models - I: Gaussian, Exponential and Beta distributions. Weibull and Pareto distributions
Reading: SR Models Chapters 2.3-2.4, 5.2, SR Prob 5.1-5.7, Lecture slides for details on various models
Problem Set: SR Models Chapter 2 - Questions 30, 33, 34, 35, 37, 48, 53 and 74, and SR Prob. Theoretical Exercise from Chapter 4, Questions 2, 4, 14 19.
Topics: Continuous Models - II: Moments, Inequalities and the moment generating function
Reading: SR Models 2.6, SR Prob 7.1-7.4
Problem Set: SR Models Chapter 2, Questions 80, 81, 82, 93, 74, 76, 77
Topics: Conditional Expectation: Definition, properties, computing expectation by conditioning, conditional expectation as a random variable, conditional expectation as a "least-squares" predictor.
Reading: SR Models 3.1-3.5, SR Prob 7.5, 7.6 and 7.9.
Problem Set: Solve homework questions, Problems 33, 43, 44, 46, 58, 72, 77, 78, 79 from SR Models, Chapter 3.
Topics: Multivariate random variables, joint pdf and cdf, conditional densities
Topics: Multivariate Models: Multinomial, Diriechlet, Multivariate Gaussian and Elliptical distributions (time permitting)
Reading: SR Models 2.5, SR Prob Chapter 6, Examples 1-7
Problem Set: SR Prob. Chapter 6, Problems 7-10, 14, 15, 20, 21, 22, 38, 40, 41, 43, 53, 54. SR Prob. Chapter 6, Theory Exercises 11, 12, 25
Topics: Limit Theorems: modes of convergence of random variables, Law of Large Numbers, Central limit theorem, confidence intervals and output analysis (time permitting), review (R-implementation of review problem available here)
Reading: SR Models 2.7, Lecture slides.
Problem Set: Solve homework questions, and play around with the R-code implementation.
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Textbooks:
1) Introduction to Probability Models: Sheldon Ross (12th ed.)
2) A first course in Probability: Sheldon Ross (8th ed.)
References: As given in the slides/in class