Probability Distributions¶
Year 1 · Block 2b · Probability and statistics
From joint distributions and MGFs through conditional expectation to laws of large numbers and normal approximations.
- 7 weeks
- 59 concept pages
Practise¶
Weeks¶
1Discrete joint distributions and MGFs38 concepts
- Binomial Theorem
- Conditional Probability Probability Theory for EOR
- Cumulative Distribution Function Probability Theory for EOR
- Discrete Random Variable Probability Theory for EOR
- Discrete Uniform Distribution Probability Theory for EOR
- Exponential Limit
- Geometric Series Math I: Calculus
- Independent Events Probability Theory for EOR
- Independence of Discrete Random Variables Probability Theory for EOR
- Indicator Random Variable Probability Theory for EOR
- Joint CDF of Discrete Random Variables
- Poisson Distribution Probability Theory for EOR
- Poisson Merging
- Probability Density Function Probability Theory for EOR
- Probability Mass Function Probability Theory for EOR
- Support of a Random Variable Probability Theory for EOR
- Taylor Series Math III: Analysis
- Bernoulli Distribution Probability Theory for EOR
- Binomial Distribution Probability Theory for EOR
- Expectation Probability Theory for EOR
- First Success Distribution Probability Theory for EOR
- Fundamental Bridge Probability Theory for EOR
- Geometric Distribution Probability Theory for EOR
- Joint Probability Mass Function
- Linearity of Expectation Probability Theory for EOR
- LOTUS (discrete and continuous) Probability Theory for EOR
- Marginal Probability Mass Function
- Moment
- Moment Generating Function
- Moments from the MGF
- Two-Dimensional LOTUS for Discrete Variables
- Uniqueness of Moment Generating Functions
- Variance and Standard Deviation Probability Theory for EOR
- Conditional Probability Mass Function
- Location and Scale Property of the MGF
- MGF of an Independent Sum
- Chicken–Egg Theorem
- Poisson Splitting
Review week 1 in Concept Finder 38 concepts
2Continuous joint distributions and dependence21 concepts
- Continuous Random Variable Probability Theory for EOR
- Covariance
- Exponential Distribution Probability Theory for EOR
- Independence of Discrete Random Variables Probability Theory for EOR
- Joint CDF of Continuous Random Variables
- Joint Probability Density Function
- LOTUS (discrete and continuous) Probability Theory for EOR
- Marginal Probability Density Function
- Memoryless Property Probability Theory for EOR
- Multinomial Distribution
- Generalized Inverse CDF Probability Theory for EOR
- Survivor Function
- Two-Dimensional LOTUS for Continuous Variables
- Uniform Distribution Probability Theory for EOR
- Realizability of a CDF Probability Theory for EOR
- Conditional Probability Density Function
- Continuous Law of Total Probability
- Correlation
- Bayes and Total Probability: Four Forms
- Conditional Cumulative Distribution Function
- Continuous Bayes Rule
Review week 2 in Concept Finder 21 concepts
3Transformations, convolution, and order statistics6 concepts
- Convolution of Independent Random Variables
- Density of an Order Statistic
- Partition of the Sample Space Probability Theory for EOR
- Sum of Two IID Uniform Variables
- Change of Variables in One Dimension Probability Theory for EOR
- Law of Total Probability Probability Theory for EOR
Review week 3 in Concept Finder 6 concepts
4Conditional expectation7 concepts
- Conditional Density Given an Event
- Conditional Expectation Given a Random Variable
- Conditional Expectation Given an Event Probability Theory for EOR
- Law of Total Expectation over a Partition
- Taking Out What Is Known
- Adam’s Law: Total Expectation
- Conditional Expectation and Independence
Review week 4 in Concept Finder 7 concepts
6Conditional variance and background information5 concepts
- Adam’s Law with Extra Conditioning
- Conditional Variance Given a Random Variable
- Eve’s Law: Total Variance
- Total Probability with Extra Conditioning
- Conditioning Trick for Variance
Review week 6 in Concept Finder 5 concepts
7Inequalities and laws of large numbers10 concepts
- Almost Surely
- Almost-Sure Convergence
- Cauchy–Schwarz Inequality for Random Variables
- Chebyshev Inequality
- Convergence in Probability
- Generalized Markov Inequality
- Jensen Inequality
- Strong Law of Large Numbers
- Weak Law of Large Numbers
- Chernoff Bound
Review week 7 in Concept Finder 10 concepts
8Distributional limits and normal approximations4 concepts
- Continuity Correction
- Convergence in Distribution
- Central Limit Theorem
- Normal Approximation to the Binomial
Review week 8 in Concept Finder 4 concepts
Supporting concepts2 concepts
Concepts appear in the week that introduces them, foundations first. 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.3 courses
- Expectation
- Variance and Standard Deviation
- Cumulative Distribution Function
- Probability Density Function
- Conditional Probability
- Binomial Distribution
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+25 moreShow fewer
- LOTUS
- Poisson Distribution
- Linearity of Expectation
- Probability Mass Function
- Bernoulli Distribution
- Discrete Random Variable
- Discrete Uniform Distribution
- First Success Distribution
- Fundamental Bridge
- Geometric Distribution
- Independent Events
- Indicator Random Variable
- Support of a Random Variable
- Independent Random Variables
- Random Variable
- Independent and Identically Distributed Random Variables
- Standard Normal Distribution
- Binomial Coefficient
- Conditional Expectation Given an Event
- Event
- Law of Total Probability
- Order Statistic
- Partition of a Set
- Probability Function
- Uniform Distribution
Also: Taylor Series (Math III: Analysis)
Where it leadsLater courses on the wiki that build on these concepts.2 courses
AchievementsCourse challenges and how many learners hold them
How to read this courseNotation, shared pages and conventions
Notation: ; geometric variables count failures before success; exponential and gamma parameters are rates; the second normal parameter is variance.
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.
The course has no separate Week 5 concept list; its week numbering is kept.
Aliases: PD
Last updated: 26 October 2026 00:09