Probability & Statistics - bsiever/WUSTL-CSE-Curriculum GitHub Wiki

Required By:

CSE 416A, CSE 417T, CSE 511A, CSE 514A, CSE 516A, CSE 518A, CSE 538T, CSE 577M

1. Potential Learning Outcomes

  • Apply key concepts of probability, including discrete and continuous random variables, probability distributions, conditioning, independence, expectations, and moments.
  • Define and explain the different statistical distributions (e.g., normal, log-normal, Poisson, Weibull) and the typical phenomena that each distribution often describes.
  • Apply the basic rules and theorems in probability including Bayes’s theorem and the Central Limit Theorem (CLT).
  • Define and demonstrate the concepts of estimation and properties of estimators.
  • Apply the concepts of interval estimation and confidence intervals.
  • Apply the concepts of hypothesis testing and p-value.
  • Apply the method of least squares to estimate the parameters in a regression model.

Other Potential Learning Outcomes

  • Basic probability axioms and rules and the moments of discrete and continuous random variables as well as be familiar with common named discrete and continuous random variables.
  • How to derive the probability density function of transformations of random variables and use these techniques to generate data from various distributions.
  • How to calculate probabilities, and derive the marginal and conditional distributions of bivariate random variables.
  • Discrete time Markov chains and methods of finding the equilibrium probability distributions.
  • How to calculate probabilities of absorption and expected hitting times for discrete time Markov chains with absorbing states.
  • How to translate real-world problems into probability models.

2. Topics Covered

Probability, Permutations & Combinations General Rules, Conditional Prob., Independence Bayes Theorem Discrete Random Variables, Probability Densities, CDF Probability Density Functions, Cumulative Density Functions, Mean, Variance, Standard Deviation Geometric Distribution, Moment generating functions Binomial, Negative Binomial Distributions Continuous Densities, Mean, Variance, Std. Dev, Moment Generating Functions Gamma, Exponential and Normal distributions Chebyshev's Inequality, Normal Approximations, Weibull distribution Expectation, Covariance, Correlation Conditional Densities, Regression Curves, Transformation of Variables Point Estimation Central Limit Theorem Confidence Intervals Estimating and Testing Hypothesis on a Proportion Regression and Least-Squares Estimators Properties of Estimators Confidence Interval Estimation and Hypothesis Testing

3. WashU Courses

3.1 ESE 326 (others: Math 3200 --> TODO: check content/learning outcomes)

Content Covered

Fall 2017:

Study of probability and statistics together with engineering applications.

  • Probability and statistics:
    • random variables
    • distribution functions
    • density functions
    • expectations, means, variances,
    • combinatorial probability, geometric probability, conditional probability
    • normal random variables, joint distribution, independence, correlation,
    • Bayes theorem, the law of large numbers, the central limit theorem
  • Applications:
    • reliability, quality control, acceptance sampling, linear regression
    • design and analysis of experiments, estimation, hypothesis testing.
Pedagogy / Delivery
Learning Outcomes

3.2 Math 3200 - Elementary to Intermediate Statistics and Data Analysis Spring 2019

Content Covered
  • An introduction to probability and statistics
    • Discrete and continuous random variables
    • Mean and variance
    • Hypothesis testing and confidence limits,
    • Student's-t distribution, Bayesian inference,
    • linear regression, single factor analysis of variance, nonparametric methods.
  • Statistical software is also introduced (SAS and R)
Pedagogy / Delivery

Lecture three times a week for 50 minutes

3.3 Comparison of ESE 326 and MATH 3200:

  • The course content is fairly similar. ESE 326 might be a better fit for the CS students with a bit more focus on the applications of probability and statistics. Students in ESE 326, however, are not exposed to statistical software such as SAS and the programming language R.

4. Peers

4.1 Peer 1

Stanford: http://web.stanford.edu/class/cs109/

Topics: combinatorics, random variables, mean and variance, independence, probability distributions, Bayes' theorem, central limit theorem, law of large numbers, hypothesis testing.

Why have a CS specific prob/stats course: 1/3 of class devoted to applying these concepts in ways relevant to CS: hashing, data analysis, inference, and machine learning

4.2 Peer 2

CMU - Probability and computing http://www.cs.cmu.edu/~harchol/PnC/class.html Part I : Probability on events. Everything about discrete random variables and continuous random variables, higher moments, conditioning, Bayes, Laplace transforms, z-transforms, tails, dominance. Simulation of random variables. Heavy-tailed distributions.

Part II : Concentration inequalities: Markov, Chebyshev, Chernoff Bounds. Introduction to randomized algorithms (both Las Vegas and Monte Carlo). Includes randomized algorithms for: sorting, min-cuts, balls-and-bins, matrix-multiplication checking, primality testing, hashing, tournament ranking, and more.

Part III : Discrete-time Markov Chains (with ergodicity proofs) and Continuous-time Markov chains. Poisson process. Tons of computer systems applications. Elementary queueing theory with applications to modeling web server farms, routers, networking protocols, and capacity provisioning for data centers.

5. Identified Missing Content/Learning Outcomes (TODO)

I suggest that after we identified the content, we can have a small targeted survey/chat with instructors of upper level courses to gauge what, if anything, is missing.