Erick C. Jones Jr., PhD, PE

Engineering Probability

Teaching · IE 3301 · UT Arlington · 2021–

How to apply probability and statistics to a wide range of problems in engineering, sustainability and life, with applications in random processes, reliability, inventory systems and queuing.

Interactive worked examples →
Interactive: explore distributions, watch the central limit theorem, build a correlation, see Type I and II errors and power, fit a regression by clicking, and run a 2×2 experiment.

Topics

How it is taught and assessed

Tools. Statistical analysis in Python (pandas, SciPy and statsmodels) or R, and in spreadsheets such as Excel.

Textbook

Probability and Statistics for Engineers and Scientists, 9th edition, Walpole, Myers, Myers and Ye available through the UTA library

Key concepts

Short definitions of the ideas the course is built on.

Random variable
A number whose value depends on chance, described by its distribution: discrete (counts) or continuous (measurements).
Conditional probability
The probability of A given that B has happened: P(A | B) = P(A and B) / P(B).
Expected value and variance
The long-run average of a random variable, and how widely it spreads around that average.
Confidence interval
A range built from a sample that, over many samples, would contain the true parameter a stated share of the time.
Prediction interval
A range where the next single observation is likely to fall; wider than a confidence interval for the mean.
Type I and Type II errors
Type I: rejecting a true null hypothesis, with probability α. Type II: failing to reject a false one, with probability β. The power of a test is 1 − β.
p-value
Assuming the null hypothesis is true, the probability of a result at least as extreme as the one observed.

Code examples

In Python and in R, step by step, with a switch to show either or both. Read them here, or download a notebook and run it.

Free tools and readings

Open and free resources used in or alongside the course.

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Tools

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