Probability Theory for EOR¶
Year 1 · Block 1b · Probability and statistics
From sample spaces and counting to random variables, expectation and Poisson processes.
- 6 weeks
- 81 concept pages
Practise¶
Weeks¶
1Sample spaces, counting and naive probability16 concepts
- Combination
- Counting
- k-Permutation
- Multiplication Rule for Counting
- Outcome
- Sample Space
- Sampling With and Without Replacement
- Stars and Bars
- Binomial Coefficient
- Event
- Naive Probability
- Union and Intersection of Events
- Complement of an Event
- Disjoint Events
- Axioms of Probability
- Birthday Problem
Review week 1 in Concept Finder 16 concepts
2Conditional probability and independence11 concepts
- Disjoint Events
- Partition of a Set
- Axioms of Probability
- Probability Function
- Conditional Probability
- Inclusion-Exclusion Principle
- Independent Events
- Law of Total Probability
- Bayes Rule
- Conditional Independence
- Prosecutor's Fallacy
Review week 2 in Concept Finder 11 concepts
3Discrete random variables and distributions19 concepts
- Hypergeometric Distribution
- Random Variable
- Discrete Random Variable
- Discrete Uniform Distribution
- Distribution
- Function of a Random Variable
- Generated Event
- Independent Random Variables
- Indicator Random Variable
- Mixture Distribution
- Probability Mass Function
- Support of a Random Variable
- Bernoulli Distribution
- Binomial Distribution
- Cumulative Distribution Function
- First Success Distribution
- Geometric Distribution
- Independent and Identically Distributed Random Variables
- Negative Binomial Distribution
Review week 3 in Concept Finder 19 concepts
4Expectation and variance18 concepts
- Bernoulli Distribution
- Expectation
- Function of a Random Variable
- Independent Random Variables
- Indicator Random Variable
- Linearity of Expectation
- LOTUS
- Mixture Distribution
- Monotonicity of Expectation
- Poisson Distribution
- Sum of Independent Random Variables
- Variance and Standard Deviation
- Conditional Expectation Given an Event
- Conditional Variance Given an Event
- First Success Distribution
- Fundamental Bridge
- Geometric Distribution
- Negative Binomial Distribution
Review week 4 in Concept Finder 18 concepts
5Continuous random variables and the normal distribution16 concepts
- Absolutely Continuous Distribution
- Continuous Random Variable
- Order Statistic
- Point Mass
- Probability Density Function
- Quantile Function
- Random Interval
- Rayleigh Distribution
- Standardization
- Support of a Random Variable
- Transformation of a Continuous Random Variable
- Uniform Distribution
- Universality of the Uniform and CDF Realizability
- Normal Distribution
- Standard Normal Distribution
- Folded Normal Distribution
Review week 5 in Concept Finder 16 concepts
6Waiting times, Poisson processes and summary measures16 concepts
- Discrete Uniform Distribution
- Exponential Distribution
- Half-Life
- Median
- Memoryless Property
- Minimum of Independent Exponentials
- Mode
- Normal Distribution
- Poisson Distribution
- Stochastic Process
- Summary Measures of a Distribution
- Symmetric Distribution
- Unimodal and Multimodal Distribution
- Lognormal Distribution
- Poisson Process
- Arrival Rate
Review week 6 in Concept Finder 16 concepts
Concepts appear in the week that introduces them, foundations first. Week titles summarise the concepts tagged to each week; a course name after a concept marks a page from another course used that week.
More about this course¶
Before you startEarlier concepts these pages use most. If a step feels unfamiliar, revisit them first.2 courses
- Set
- Exponential Function
- Definite Integral
- Function
- Intersection of Sets
- Factorial
-
+16 moreShow fewer
Where it leadsLater courses on the wiki that build on these concepts.5 courses
- Expectation
- Variance and Standard Deviation
- Cumulative Distribution Function
- Independent Random Variables
- Probability Density Function
- Random Variable
-
+16 moreShow fewer
- Conditional Probability
- Independent and Identically Distributed Random Variables
- Binomial Distribution
- LOTUS
- Poisson Distribution
- Standard Normal Distribution
- Binomial Coefficient
- Conditional Expectation Given an Event
- Event
- Law of Total Probability
- Linearity of Expectation
- Order Statistic
- Partition of a Set
- Probability Function
- Probability Mass Function
- Uniform Distribution
- Expectation
- Variance and Standard Deviation
- Cumulative Distribution Function
- Independent Random Variables
- Mixture Distribution
- Point Mass
-
+11 moreShow fewer
- Poisson Distribution
- Probability Density Function
- Absolutely Continuous Distribution
- Conditional Probability
- Indicator Random Variable
- Probability Mass Function
- Bernoulli Distribution
- Discrete Random Variable
- Independent and Identically Distributed Random Variables
- Negative Binomial Distribution
- Poisson Process
Also: Stochastic Models (via Conditional Probability)
AchievementsCourse challenges and how many learners hold them
How to read this courseNotation, shared pages and conventions
Shared Probability Theory and Probability Distributions concepts have one canonical page here. Those pages keep both courses’ tags and source references, and the Probability Distributions homepage lists them in its weeks alongside its advanced topics.
A density is fixed only up to its values on a set of zero length (zero area for joint densities), for example at finitely many points: changing it there changes no probability. Identities between densities on these pages therefore hold except possibly on such a set.
For teachers and tutorsPrepare the connections for your next explanation
Choose a concept for your next explanation. Review its recorded foundations and later uses, then check the concept page's sources against your own course material.
The workbench uses published prerequisite links. It describes concept relationships; class performance and teaching coverage need separate evidence.
Aliases: PT, Probability Theory
Last updated: 26 October 2026 00:09