Probstat

This is a course web page for the course Probability and Statistics for Computer and Software Engineers.

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Materials

Many of the exercises are taken from various sources, listed here: FCP = Ross, A First Course in Probability, Macmillan, 1984; SPS = Spiegel, Schiller, Srinivasan, Schaum's outlines Probability and Statistics Fourth Edition. Mc-Graw-Hill, 2013; IPSES = Ross, Introduction of Probability and Statistics for Engineers and Scientists, Wiley, 1987.

Homework

• Homework 1 due 9/23.
• Homework 2 due 12/7.
• Homework 3 due 12/26. (but should be very useful for preparing for the final examination)

Class activities / project

• How to submit class activities due 12/20.
• How to submit your project TBA.

Week1

• Introduction VDO: youtube
• Coin Toss Experiments (Practice 1)
• Fun with statistics 1 (Practice 2)
• Basic concepts
  • Part 1: Outcomes, Sample Spaces, and Events
  • Part 2: Conditional probability (1)
• Random word practice 1 (Practice 3)

Week2

• Basic concepts
  • Part 3: Conditional probability (2) -- The clip contains errors at the end. Please see the annotations.
• Counting
  • Part 1: Basic principles of counting
  • Part 2: Permutations and Combinations Part 2.1, Part 2.2, Part 2.3
• Week2 Practice 1
• Axioms of probability: youtube
• Conditional probability: part3

Week3

• Class cancelled: Tuesday 9/2.
• Conditional probability (revisited):
  • Independent events: youtube
  • Bayes' formula: part 1, part 2
• Homework 1

Week4

• Random variables:
  • Part 1
  • Part 2.1 - Expectations, balls and bins experiment
  • Part 2.2 - Warm-up problems
  • Part 2.3 - First Trial to Compute the Expectation
  • Part 2.4 - The expected number of empty bins
• Week4 Practice 1
• Variances: Part 1, Part 2
• Week4 Practice 2 -- E[X²].
• (Watch this later.) Proof of the linearity of expectation: youtube

Week5

• Analysis of the fullest bins: Part 1, Part 2, Part 3
• Examples on variances
• Important types of discrete random variables
  • Binomial random variables
  • Geometric random variables
• Week5 Practice 1
• Independent random variables: Part 1, Part 2
• Week5 Practice 2

Week6

• Week6 Practice 1 - experiments on variances
• Random experiments: (watch these and work on practice 2).
  • The birthday problem: part 1, part 2
  • The coupon collector's problem: part 1, part 2
• Week6 Practice 2

Week7

• Markov's Inequality: part 1, part 2
• Continuous random variables: part 1, part 2

Week8

• Week8 Practice 1 -- practice on continuous random variables
• Normal random variables: part 1, part 2
• Week8 Practice 2 -- normal random variables

Week9

• Poisson random variables: part1, part2

Week10

• Exponential random variables: part1, part2, part3
• Week10 practice 1 -- Poisson and exponential random variables & simulations

Week11

• Jointly distributed random variables
• Sample means and sample variances. notes
• Week11 practice 2 -- Sample means, sample variances, confidence interval

Week12

• More on sample distributions and confidence intervals: notes

Week13

• Estimations: method of moment estimations, maximum likelihood estimators
• Hypothesis testing
  • Practice 1

Week14

• Regression
  • practice

Week15

• Analysis of variances
  • Practice 1
• Limit theorems

Lecture notes

These notes are meant to be used in complement to the video lectures. They only contain summary of the materials discussed in the video. Don't use them to avoid watching the clips please.

• Basic concepts
• Counting
• Random variables
• Balls-and-bins experiment and linearity of expectation
• Variances
• Special random variables
• Poisson and exponential random variables
• Jointly distributed random variables
• Sample means and sample variances
• Confidence intervals
• Chi-squared distribution
• Dealing with unknown variances (t-distribution)
• Parameter estimations
• Hypothesis testing
• Regression
• Analysis of variance
• Limit theorems

Topics

• Course introduction
• Probability theory
  • Introduction to various concepts in probability theory
  • Elements of probability: axioms of probability, conditional probability, independence, Bayes' formula
  • Discrete random variables and expectations: random variables, expected values, variances, jointly distributed random variables
  • Tail bounds and analysis of randomized algorithms
  • Continuous random variables
• Statistics
  • Sampling
  • Parameter estimation
  • Hypothesis testing
  • Regression
  • Analysis of Variance

Administrative information

• Score breakdown: in-class activities 19%, projects 27%, midterm exam 27%, final exam 27%