Probability and Statistics Guidelines for Incoming Students

The Systems Engineering Program requires an undergraduate level Probability and Statistics prerequisite for students enrolling in the M.Eng. program. We have identified the material that is a necessary prerequisite for our classes. This information is a guideline for the probability and statistics concepts that we feel every student should understand in order to be successful in our courses. It is important for every student to review this list as some undergraduate courses may only cover probability or only cover statistics, but it is important that our students are comfortable in their knowledge of both.

The key question in determining the suitability of your knowledge from having taken or planning to take a particular course(s) is partially summed by the following quote from a report from the American Statistical Association (Guidelines for Assessment and Instruction in Statistics Education):
“Some people teach courses that are heavily slanted toward teaching students to become statistically literate and wise consumers of data; this is somewhat similar to an art appreciation course. Some teach courses more heavily slanted toward teaching students to become producers of statistical analyses; this is analogous to the studio art course.”

What you will need for Cornell Master of Engineering classes is the latter, analogous to the studio course. Some classes offered at Cornell that we consider to offer the appropriate preparation are ENGRD2700 and CEE3040. For your reference, the items covered in ENGRD2700 are listed below. We also feel that the textbook by Jay Devore, “Probability and Statistics for Engineering and the Sciences” (any edition) is at the level that is needed for our classes. Thus, if you are getting ready to take our classes you might want to review that book to be sure that you feel comfortable with
material at the appropriate level.

Students who are uncertain about their skill level, perhaps because significant time has passed since they have taken courses that covered this material, are strongly encouraged to take the self-assessment exam. Please review the solutions to the self-exam here.

This exam can help you self-identify whether you should take another course, such as ENGRD2700 which is offered as a distance-learning course over the summer, or perhaps participate in “Probability and Statistics Bootcamp” during winter session, which is made freely available and is non-credit bearing but assumes the audience is not new to the material.

Ultimately, the Cornell Systems Engineering program is designed and dedicated to the success of our students. Hence, we are glad to honor resources like this requirements list, the self-assessment test, the Winter Session Bootcamp, and ENGDR2700 to help all students in the way that will help them most.

Cornell University ENGRD 2700 Basic Probability and Statistics for Engineers

Contents

  1. Introduction and Motivation
    • Intro, What the course is about, Overview
  2. Exploratory Data Analysis: Describing Sample Data
    • Graphical displays
    • Numerical summaries
  3. Counting and Probability
    • Counting: Product rule, sampling with replacement, without, combs, practice problems
    • Probability: Elements, Events, Probability functions, specifying, properties, equal probs, hypergeometric
  4. Conditional Probability, Bayes’ Rule and Independence
    • Cond Prob, Law of total prob, Bayes rule, independence
  5. Random Variables
    • Definition, Probability mass function, Cumulative distribution function, expectation, variance
  6. Special Discrete Random Variables
    • Bernoulli, binomial, Poisson, geometric, hypergeometric
  7. Continuous Random Variables
    • Density, cumulative distribution function, percentiles, expectation, variance,
  8. Special Continuous Random Variables
    • Uniform, exponential, Weibull, beta, gamma, normal, lognormal
  9. Probability Plots
  10. Multiple Random Variables
    • Definition, independence, conditional distrib, more than two
  11. Covariance and Correlation Expectation, covariance,
    • correlation
  12. Sampling Distributions
    • Inference, sampling, sums and averages, CLT
  13. Interval Estimation
    • Confidence intervals (CI) for mean, for proportion, two independent samples, two props, paired samples, CIs for variance
  14. Hypothesis Tests
    • Normal means, Type I and II errors, relation to confidence intervals, two populations
  15. Regression
    • Simple linear
    • confidence intervals and testing for beta_1
  16. More Regression
    • Transformation of vars
    • Multiple linear
    • Logistic regression

Additionally, all students should have a basic understanding of calculus and mathematics.