2DI90 - Probability and Statistics

### Course slides

Links for the course materials will be posted in a timely fashion. For your convenience I'm posting all the slides already - but I may change slightly as the course progresses.

Below you'll find the contents covered in each lecture, and well as the corresponding sections of the textbook.

Slides chapter 2: 2DI90_ch2.pdf Slides chapter 3: 2DI90_ch3.pdf
Slides chapter 4: 2DI90_ch4.pdf (optional slides on integral calculus: 2DI90_integral_calculus_review.pdf )
Slides chapter 5: 2DI90_ch5.pdf
Slides Simulation: 2DI90_simulation.pdf (slides only, no textbook material)
Slides chapter 6: 2DI90_ch6.pdf
Slides chapter 7: 2DI90_ch7.pdf
Slides chapter 8: 2DI90_ch8.pdf
Slides chapter 9: 2DI90_ch9.pdf
Slides chapter 11: 2DI90_ch11.pdf

# WEEK 1 Lecture 1 (April 25)
• Before we start - Logistical Remarks
• Why Probability (and Statistics) - An Introduction
• Sample spaces and events (MR 2.1)
• Counting techniques
• The concept of Probability (MR 2.2)
• Axioms of Probability
• Algebraic rules for probabilities
• Conditional Probability (MR 2.4)
• Multiplication and total probability rules (MR 2.5)
• Independence (MR 2.6)
• Bayes' Theorem (MR 2.7)
• Examples and Discussion
• Introduction to Random Variables (MR 2.8)
- Slides: 2DI90_ch2.pdf
- Intermezzo: intermezzo1.pdf

# WEEK 2 Lecture 2 (May 2)
• Definition of Random Variables (MR 2.8)
• Continuous vs. Discrete
• Discrete Random Variables (MR 3.1)
• Probability Mass Function (MR 3.2)
• Cumulative Distribution Function (MR 3.3)
• Mean and Variance (MR 3.4)
• Functions of random variables
• Independence of Random Variables (MR 5-1.4)
• Mean and Variance of sums of independent random variables (without proof)
• Specific discrete distributions
• Uniform (MR 3.5)
• Bernoulli (MR 3.6)
• Bernoulli trials
• Binomial (MR 3.6)
• Tables and Computational Tools for the evaluation of event probabilities.
• Geometric (MR 3.7)
• Memoryless property
- Slides: 2DI90_ch3.pdf
- Intermezzo: Computational_Intermezzo.pdf and demo1.R

# WEEK 3 Lecture 3 (May 9)
• Specific discrete distributions
• Negative Binomial (MR 3.7)
• Hypergeometric Distribution (MR 3.8)
• The Poisson Distribution (MR 3.9)
• The relation between Binomial and Poisson distributions
• Introduction to Continuous Random Variables
• Continuous Random Variables (MR 4.1)
• Probability Density Function (MR 4.2)
• Some Important Properties
• Cumulative Distribution Function (MR 4.3)
• Mean and Variance of Continuous Random Variables (MR 4.4)
• Many Examples
• Specific Continuous Distributions
• Uniform Distribution (MR 4.5)
• Normal Distribution (MR 4.6)
• Motivation and some properties
• The standard normal distribution
• Basic Properties
- Slides: 2DI90_ch3.pdf and 2DI90_ch4.pdf (up to slide 36)
- Intermezzo: intermezzo_2.pdf Lecture 4 (May 12)
• The standard normal distribution
• Basic Properties
• Standardizing a Normal random variable
• Using probability tables and computational tools
• The Exponential Distribution (MR 4.8)
• The Poisson Process (not clearly explained in the book)
• Specific Continuous Distributions
• The Poisson Process (not clearly explained in the book)
• Erlang Distribution (MR 4.9)
- Slides: 2DI90_ch4.pdf

# WEEK 4 Lecture 5 (May 16)
• Weibull Distribution (MR 4.10)
• Joint Probability Distributions (discrete case) (MR 5.1)
• Joint Probability Mass Functions
• Marginal p.m.f.'s
• Conditional p.m.f.'s
• Independence of random variables (MR 5-1.4 and 5-1.5)
• Examples
• Continuous random variables (only basic ideas)
• Means, Variances, Covariances and Correlation (MR 5-2)
• Correlation and independence are not the same thing - example
• Linear Functions of normal random variables (MR 5-4)
• The Law of Large Numbers (not stated in the book)
- Slides: 2DI90_ch4.pdf and 2DI90_ch5.pdf
- Intermezzo: intermezzo_3.pdf and invest.R Lecture 6 (May 19)
• The Central Limit Theorem (stated only in page 239 of MR)
• The normal distribution as an approximation of (MR 4-7)
• Binomial distribution
• Poisson distribution
• Introduction to Simulation and Monte Carlo methods
• Historical Notes
• Pseudo-Random Sequences
• Simulating Random Variables
• Discrete Random Variable
• Generating Bernoulli Random Variables
• Generating Binomial, Geometric and Negative Binomial Random Variables
• Generating arbitrary discrete random variables
• Simulating Random Variables
• Continuous Random Variables
• Inverse Transform Method
- Slides: 2DI90_ch5.pdf and 2DI90_simulation.pdf

# WEEK 5 Lecture 7 (May 23)
• Simulating Random Variables
• Continuous Random Variables
• Rejection Method
• Addressing Complicated Problems with Simulation
• Estimating Probabilities
• Approximate analysis using the CLT
• Conservative results using Chernoff's bound
• Estimating Means and Variances
• Approximate analysis using the CLT
• What is Statistics?
• Descriptive Statistics: Numerical vs. Graphical Representations (MR Chapter 6)
• Numerical Summaries of Data
• The Histogram and Frequency Distributions
- Slides: 2DI90_simulation.pdf and 2DI90_ch6.pdf
- Intermezzo: simulation_lab_guide.pdf

# WEEK 6 Lecture 8 (May 30)
• Descriptive Statistics: Numerical vs. Graphical Representations (MR Chapter 6)
• Numerical Summaries of Data
• The Histogram and Frequency Distributions
• The Box-Plot
• Time-Sequence Plots
• Quantile-Quantile Plots
(The above were only covered in the video-lecture)
• Introduction to Point Estimation (MR 7.1)
• The Notion of a Random Sample (MR 7.2)
• Estimators and Estimates (MR 7.2)
• Criteria for the Evaluation of Estimators (MR 7.3)
• Mean Squared Error (MSE)
• Bias, Variance, and Standard Error
• Bias-Variance decomposition Lecture 9
• Methods of Point Estimation (MR 7.4)
• Method of Moments (MR 7.4.1)
• Maximum Likelihood Estimation (MR 7.4.2)
- Slides: 2DI90_ch6.pdf and 2DI90_ch7.pdf (up to slide 40)
- Files and code used in for the slides of chapter 6: Golf_example.R ; Example_6.15.R ; PSI20.R and PSI20.txt Lecture 10 (June 2)
• Recap of the Method of Moments and Maximum Likelihood Estimation
• Important Examples
• Beyond the random sample case - an example
• Introduction to Interval Estimators and Confidence Intervals (MR 8.1)
- Slides: 2DI90_ch7.pdf and 2DI90_ch8.pdf (up to slide 6 only)

# WEEK 7 Lecture 11 (June 6)
• Confidence Intervals for the mean when variance in known (MR 8.1)
• One and two-sided intervals
• Choice of sample size
• Approximate Confidence Intervals for large samples (MR 8-1.5)
• Confidence Intervals for the mean when the variance is unknown (MR 8.2)
• Confidence Intervals for the variance and standard deviation (MR 8.3)
• Confidence Intervals for proportions (MR 8.4)
• Prediction Intervals (MR 8-7.1)
• Introduction to Hypothesis Testing (MR 9.1)
• Statistical Hypothesis
• Tests and Tests Statistics
• Type I and Type II errors
- Slides: 2DI90_ch8.pdf
- Scripts: CI_example.R ; z-intervals.R ; unknown_variance_CI.R ; quantile_computation.R ; class_problem.R ; datasets.zip Lecture 12 (June 9)
• Introduction to Hypotheses Testing (MR 9.1)
• P-Values
• Some Useful Tests
• Tests for the mean, known variance (MR 9.2)
• Choice of Sample Size (MR 9-2.2)
• Large Sample Tests (MR 9-2.3)
• Tests for the mean, unknown variance (MR 9.3)
- Slides: 2DI90_ch9.pdf

# WEEK8 Lecture 13 (June 13)
• Tests for the variance (MR 9.4)
• Tests for the proportions
• Goodness-of-Fit (GoF) tests for normality
• Introduction to Linear Regression (MR 11.1)
• Simple Linear Regression (MR 11.2)
• Properties of Least Squares Estimators
- Slides: 2DI90_ch9.pdf and 2DI90_ch11.pdf
- Scripts: hypothesis_testing_example.R ; Pearson_chi_square_tests.R
class_assignment_2.R ; regression_example.R Lecture 14 (June 16)
• Properties of Least Squares Estimators
• Hypothesis Testing for Linear Regression Models
• Approach based on t-tests
• ANOVA approach
• Confidence Intervals for the parameters in Linear Regression Models
• Confidence Intervals for the Mean Response
• Prediction of New Observations
• Adequacy of the Regression Model
• Residual Analysis
• Coefficient of Determination
• Final Remarks
- Slides: 2DI90_ch11.pdf
- Scripts: regression_example.R

# WEEK 9 Lecture 15 (June 20)

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Last change: Tue Jun-20-17 12:40:07
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