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IntroductionToProbabilityPy

Jupyter notebooks with the Python equivalent to the R code sections in Blitzstein and Hwang's Introduction To Probability, Second Edition

Requirements

These Jupyter notebooks have been verified on the following Python versions:

The Anaconda Python distribution comes highly recommended, as it includes Python, the conda package manager, the Spyder integrated development environment, and a whole universe of Python packages for mathematics and engineering, including NumPy, SciPy, Matplotlib and Jupyter.

Minimum required Python packages:

Other requirements / dependencies

Executing these notebooks locally

After installing Python and Jupyter, navigate to this project's home directory where these notebooks are saved, open up a command window or shell interface, and type the following command:

 jupyter notebook

Your default browser will open up to show the Notebook Dashboard at http://localhost:8888.

MathJax is the JavaScript library Jupyter uses to render LaTeX. To ensure that you have the absolute, latest version of MathJax rendering the math in your locally-executed notebooks, set the NotebookApp.enable_mathjax configuration parameter in jupyter_notebook_config.py to point to the newest available MathJax.js version on cdnjs. (c.f. Config file and command line options, Jupyter docs).

These notebooks have been confirmed to run on:

  • Chrome 71.0.3578.98 (official build), 64-bit and Firefox 64.0, 64-bit on Windows 10
  • Chrome 69.0.3497.100 (official build, 64-bit and Firefox 52.8.0, 64-bit on Windows 7
  • Chrome 71.0.3578.98 (official build), 64-bit; Firefox 64.0 (64-bit); and Safari 12.0.2 (13606.3.4.1.4) on macOS (High Sierra, v10.13.6)

Internet Explorer is not recommended!

View these notebooks on NBViewer

  • Ch1 - Probability and Counting: Vectors; Factorials and binomial coefficients; Sampling and simulation; Matching problem simulation; Birthday problem calculation and simulation
  • Ch2 - Conditional Probability: Simulating the frequentist interpretation; Monty Hall simulation
  • Ch3 - Random Variables and their Distributions: Distributions in SciPy; Binomial distribution; Hypergeometric distribution; Discrete distributions with finite support
  • Ch4 - Expectation: Geometric, Negative Binomial, and Poisson; Matching simulation; Distinct birthdays simulation
  • Ch5 - Continuous Random Variables: Uniform, Normal and Exponential distributions; Plots in Matplotlib; Universality with Logistic; Poisson process simulation
  • Ch6 - Moments: Functions; Moments; Medians and modes; Dice simulation
  • Ch7 - Joint Distributions: Multinomial; Multivariate Normal; Cauchy
  • Ch8 - Transformations: Beta and Gamma distributions; Convolution of Uniforms; Bayes' billiards; Simulating order statistics
  • Ch9 - Conditional Expectation: Mystery prize simulation; Time until HH vs. HT; Linear regression
  • Ch10 - Inequalities and Limit Theorems: Jensen's inequality; Visualization of the law of large numbers; Monte Carlo estimate of π; Visualizations of the central limit theorem; Chi-Square and Student-t distributions
  • Ch11 - Markov Chains: Matrix calculations; Gambler's ruin; Simulating from a finite-state Markov chain
  • Ch12 - Markov Chain Monte Carlo: Metropolis-Hastings; Gibbs
  • Ch13 - Poisson Processes: 1D Poisson process; Thinning; 2D Poisson process
  • Appendix B - Python / NumPy / SciPy

Joseph K. Blitzstein and Jessica Hwang, Harvard University and Stanford University, © 2019 by Taylor and Francis Group, LLC