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Tentative Schedule:
Weeks 1-2: Basic Ideas of Probability
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Intro, Events, Sample Space, Venn Diagram
Baron 2.1-2.2; Hofmann 1.1-1.2
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Kolmogorov Axioms, Corollaries
Baron 2.2; Hofmann 1.3
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Counting
Baron 2.3; Hofmann 1.4
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Conditional Probability, Independence
Baron 2.4; Hofmann 1.5-1.7
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Bayes theorem, tree diagrams
Baron 2.4; Hofmann 1.7
Weeks 3-4: Discrete Distributions.
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Bernoulli Trials, Random Variables (RVs)
Baron 3.4.1; Hofmann 1.8, 2.2.1, 2.0
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PMF of a Discrete RV
Baron 3.1; Hofmann 2.1
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Expectation & Variance laws
Baron 3.3; Hofmann 2.1.1, 2.1.2
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Specific Discrete Families: Binomial, Geometric, Poisson
Baron 3.4; Hofmann 2.2.2, 2.2.3, 2.2.4
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Compound PMFs, Covariance, correlation
Baron 3.3.5; Hofmann 2.2.5
Weeks 5-6: Continuous Distributions.
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Continuous RVs, Probability Density Functions ( PDFs), Cumulative Distribution Functions
(CDFs)
Baron 4.1; Hofmann 2.3
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Specific Continuous Families: Uniform, Exponential, Erlang
Baron 4.2; Hofmann 2.4.1, 2.4.2, 2.4.3
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Exponential, Erlang, Poisson Connections
Hofmann 2.4.3
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Gamma Distribution
Baron 4.2.3
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Normal Distribution
Baron 4.2.4; Hofmann 2.4.4
Weeks 7-8: Simulation techniques.
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Elementary Simulation
Baron 5.3; Hofmann 3.1,3.3
Random Number Generators
Baron 5.2.1; Hofmann 3.2
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Discrete Random Variates
Baron 5.2.2; Hofmann 3.2.1
Inverse Transform Method
Baron 5.2.3; Hofmann 3.2.2
Rejection Method
Baron 5.2.4;
Solving Problems by Monte Carlo methods
Baron 5.3; Hofmann 3.3
Weeks 9-10: Stochastic processes.
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Definition
Baron 6.1; Hofmann Ch.4 Intro.
Poisson Process
Baron 6.3.2; Hofmann 4.1
Birth and Death Processes
Hofmann 4.2
Weeks 11-12: Queuing Theory
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Introduction and Notation
Hofmann Ch.5 Intro.
Model as Stochastic Processes, Little’s Law
Hofmann 5.1
Birth and Death Transition Diagrams, M/M/1 Queue
Hofmann 5.2
M/M/1/K and M/M/c Queuing systems, Erlang’s C Formula
Hofmann 5.3, 5.4
Weeks 13-15: Statistical Methods
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Basic Concepts: population, sample, parameters, statistics, sampling
Baron Ch.8 Intro., 8.1
Descriptive and graphical statistics
Baron 8.2, 8.3
Statistical Inference: Parameter Estimation, Properties of Estimators
Hofmann 6.1
Statistical Inference: Parameter Estimation, Method of Estimation: MoM and MLE
Baron 9.1 Hofmann 6.1
Statistical Inference: Confidence Intervals for Means and Proportions
Baron 9.2, 9.3 Hofmann 6.2
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Statistical Inference: Hypothesis Tests
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Simple Linear Regression
Baron 9.4 Hofmann 6.3
Baron 10.1 Hofmann 6.4
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