DTS 2263 units200 LevelSecond Semester

Probability for Data Science

B.Sc. Data Science, University of Uyo

DTS 226 (Probability for Data Science) is a 3-unit, 200 Level course taught in the Second Semester at the University of Uyo, Akwa Ibom State, Nigeria.

The mathematics of uncertainty: probability axioms, random variables, distributions, expectation, and the limit theorems. Probability is the language machine learning is written in — every model output is ultimately a probability statement.

On Areté, DTS 226 comes with

  • 2 recommended textbooks
  • an AI tutor that has read this course’s outline and notes
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Course outline

  1. 01Sample spaces, events and the axioms of probability
  2. 02Conditional probability, independence, the law of total probability and Bayes' theorem
  3. 03Discrete random variables: probability mass functions, expectation and variance
  4. 04Discrete distributions: Bernoulli, binomial, geometric, hypergeometric, Poisson
  5. 05Continuous random variables: density and distribution functions
  6. 06Continuous distributions: uniform, exponential, gamma, normal
  7. 07Joint, marginal and conditional distributions; covariance and correlation
  8. 08Transformations of random variables; moment generating functions
  9. 09Laws of large numbers and the Central Limit Theorem; introduction to Markov chains

Recommended textbooks

  • A First Course in Probability — Sheldon Ross

    10th ed. — the standard; work the problems

  • Introduction to Probability — Blitzstein & Hwang

    2nd ed. — free PDF; the Harvard Stat 110 text, with superb free video lectures

How to pass DTS 226

  • Bayes' theorem is the most important single formula in the course — it is the entire basis of Naive Bayes classifiers and of Bayesian inference
  • Watch Joe Blitzstein's Stat 110 lectures (free on YouTube); they are the best probability teaching available anywhere
  • For each distribution, learn the story that generates it ("number of successes in n trials", "waiting time until first event") — then you never have to guess which one applies
  • Draw the sample space for small problems. Most probability mistakes are modelling mistakes, not arithmetic mistakes

DTS 226 — questions and answers

What is DTS 226 at the University of Uyo?
DTS 226 (Probability for Data Science) is a 3-unit, 200 Level course taught in the Second Semester at the University of Uyo, Akwa Ibom State, Nigeria. The mathematics of uncertainty: probability axioms, random variables, distributions, expectation, and the limit theorems. Probability is the language machine learning is written in — every model output is ultimately a probability statement.
What topics are covered in DTS 226?
The DTS 226 outline covers 9 topics: Sample spaces, events and the axioms of probability; Conditional probability, independence, the law of total probability and Bayes' theorem; Discrete random variables: probability mass functions, expectation and variance; Discrete distributions: Bernoulli, binomial, geometric, hypergeometric, Poisson; Continuous random variables: density and distribution functions; Continuous distributions: uniform, exponential, gamma, normal; Joint, marginal and conditional distributions; covariance and correlation; Transformations of random variables; moment generating functions; Laws of large numbers and the Central Limit Theorem; introduction to Markov chains.
What textbooks are recommended for DTS 226?
Recommended reading for DTS 226: A First Course in Probability by Sheldon Ross; Introduction to Probability by Blitzstein & Hwang.
How do I pass DTS 226?
Bayes' theorem is the most important single formula in the course — it is the entire basis of Naive Bayes classifiers and of Bayesian inference Watch Joe Blitzstein's Stat 110 lectures (free on YouTube); they are the best probability teaching available anywhere For each distribution, learn the story that generates it ("number of successes in n trials", "waiting time until first event") — then you never have to guess which one applies Draw the sample space for small problems. Most probability mistakes are modelling mistakes, not arithmetic mistakes
Where can I find DTS 226 lecture notes and past questions?
Areté (https://www.aretecyb.tech/courses/dts-226) carries 2 recommended textbooks for DTS 226, plus an AI tutor that has read the outline. It is free for University of Uyo students — sign in with your email, no password.

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