Probability & Statistics in Engineering

Fall 2022 - 6 Sep

Introductions

Logistics

  • Office hours: Thu 10am-1pm
  • TuTh 1-2:15pm
  • Echo360 lecture recordings
  • Supplemental Instruction: Julia Leventis

Grading

   
Homework 30%
Midterm 30%
Final 35%
Quizzes 5%

Textbook

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D. Montgomery & G. Runger, Applied Probability and Statistics for Engineers, Wiley

and some additional notes on specific topics (e.g., Bayes' theorem)

Gradescope

gradescope.png https://www.gradescope.com/courses/427843

  • Disability Statement

http://www.umass.edu/disability/

  • Inclusivity

https://engineering.umass.edu/about-us/inclusivity-statement

  • Academic Honesty Policy Statement

http://umass.edu/dean_students/codeofconduct/acadhonesty/

Course objvectives

  • Understand the fundamental concepts of probability (e.g., independence, expectation, density functions)
  • Identify, apply and evaluate the proper probability model for different systems
  • Utilize statistical methods to make inferences about systems from data
  • Perform regression analyses, test hypotheses, and calculate confidence intervals for solving engineering problems
  • Acquire a basic understanding of statistical inference and sampling theory

Schedule

Week 1 Statistics in engineering
Week 2 Probability concepts
Week 3 Discrete variables
Week 4 Continuous variables
Week 5 Probability distributions
Week 6 Joint probability
Week 7 Conditional probability
Week 8 Central limit theorem; Midterm
Week 9 Point estimation
Week 10 Confidence intervals
Week 11 Hypothesis testing
Week 12 NO CLASS
Week 13 Inference for two samples
Week 14 Linear regression

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People can come up with statistics to prove anything. Forty percent of all people know that

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Engineering method

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What about uncertainty?

Uncertainty

  • Randomness with the underlying process that is exhibited as variability
  • Aleatory uncertainty
  • Inherent in nature and cannot be reduced
  • Imperfect or insufficient models of the process of interest
  • Epistemic uncertainty
  • Improved models or measurements could reduce it

Aleatory uncertainty

Variability - Randomness

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Histograms

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Joint variability

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Epistemic uncertainty

  • Predictions and analysis require models
  • All models are wrong, but some are useful
  • Reducible uncertainty as more knowledge is gained

Example

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\[ \Delta_B = \dfrac{P L^3}{3 E I}\]

  • Material is linearly elastic
  • Beam remains plane under load \(P\)
  • Support of the beam at point \(A\) is perfectly rigid

Decision making under uncertainty

  • No single observation is representative of the system
  • Evaluation or predictions are based on imperfect models
  • Statistics allow us to describe the unavoidable uncertainty
  • Make decisions based on trade offs (cost, benefit etc.)

Population and samples

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  • Mechanistic models
  • Empirical models
  • Statistical inference
  • Probability models

Readings

  • Section 1.1
  • Section 1.2.1
  • Sections 1.3-1.4