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1890 learning items

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Quiz

Statistical Independence

Distinguish statistical independence from disjointness and causal stories. Test probability tables, calculate reliability, analyze complements and selection, and build counterexamples separating pairwise from mutual independence. Prerequisites: conditional probability and multiplication rules; no inference tests or advanced stochastic-process theory are required. Includes single-select and multiselect questions with worked solutions and distractor feedback. References: [1.4.1 Product definition, multi-event definition and complements](https://www.probabilitycourse.com/chapter1/1_4_1_independence.php), [1.4.0 Definition, conditional axioms and chain rule](https://www.probabilitycourse.com/chapter1/1_4_0_conditional_probability.php).

statistics

Oct 23, 2026

25 questions

Quiz

Conditional Probability & Multiplication Rules

Learn conditional probability through restricted populations, sampling without replacement and multistage project trees. Work from direct ratios to full-history chain rules, missing branches, feasibility checks and subtle null-event distinctions. Prerequisites: event operations, probability axioms and counting. Tree branches are stated in text so every problem is self-contained. Includes single-select and multiselect questions with worked solutions and distractor feedback. References: [1.4.0 Definition, conditional axioms and chain rule](https://www.probabilitycourse.com/chapter1/1_4_0_conditional_probability.php).

statistics

Oct 23, 2026

25 questions

Quiz

Principles of Counting & Combinatorics

Choose counting methods by defining what makes two outcomes different. Practice sum and product rules, permutations, combinations, repeated letters, circular seating, labeled and unlabeled groups, stars and bars, and constrained arrangements. Prerequisites: basic algebra, sets and elementary probability rules. Worked solutions move from direct enumeration to complements, blocks, occupancy shifts and justified symmetry factors. Each explanation identifies the overcount or omitted restriction behind the distractors. Cover: Photo by Kampus Production on Pexels.

statistics

Oct 23, 2026

25 questions

Quiz

Kolmogorov's Axioms & Basic Probability Theorems

Derive and apply probability rules from nonnegativity, normalization and countable additivity. Practice complements, empty events, monotonicity, union formulas, Boole bounds and Bonferroni bounds. Prerequisite: sample spaces and event operations. Problems progress from direct calculations to checking model feasibility, reconstructing event regions and analyzing zero-probability events. Detailed solutions state the assumptions and avoid importing independence where it has not been given. Cover: Photo by Roberto Lee Cortes on Pexels.

statistics

Oct 23, 2026

25 questions

Quiz

Sample Spaces, Events & Set Operations

Build the event language needed for probability. Define sample spaces, simple and compound events, unions, intersections, complements, disjointness, partitions and De Morgan laws. Prerequisites: basic sets and logic plus the earlier data foundations. Questions progress from identifying recorded outcomes to diagnosing overlapping categories and changes of universe. Worked solutions use explicit outcomes and logical cases; no conditional-probability formulas are assumed. Cover: Photo by ClickerHappy on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Data Ethics, Privacy & Communication

Apply ethical statistical judgment to realistic data-work decisions. Examine purpose and consent, privacy and disclosure, representation and measurement bias, accessible graphics, proportionate claims, transformation records and corrections. Prerequisites: introductory data analysis and reproducible workflows. Scenarios progress toward balancing transparency with protected access and resisting misleading reporting. This set teaches professional reasoning rather than jurisdiction-specific legal advice. Cover: Photo by Rulo Davila on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Random Simulation & Reproducible Notebooks

Develop a reproducible simulation workflow using elementary R. Explore seeds, replacement, simulated proportions, variable results, scripts, project paths, data versions and clean execution. Prerequisite: basic R and validated tabular data. Questions build from individual simulation operations to reviewing hidden state, generator changes and selectively reported runs. Formal probability mechanics are reserved for later topics; explanations emphasize what the code does and what its output can support. Cover: Photo by Daniil Komov on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Import, Tidy, Join & Validate Data

Practice turning raw files into interpretable analytical tables. Study observation units, dictionaries, types, missing codes, reshaping, keys, joins, duplicates, validation and provenance. Prerequisite: beginner R and descriptive statistics. Cases progress from reading a field correctly to diagnosing row multiplication, mixed aggregation levels and misleading cleaning decisions. Worked explanations connect each transformation to the meaning of the resulting data. Cover: Photo by Rodrigo Santos on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Programming from First Principles

Learn to read and reason about basic R programs without prior coding experience. Work with objects, vectors, one-based indexing, logical filters, missing values, functions, loops and data frames. Prerequisites: arithmetic and descriptive statistics. Questions progress from individual operations to debugging and validating small reusable calculations. These are single-select and multiselect code-interpretation exercises, with step-by-step explanations of outputs and common mistakes. Cover: Photo by Markus Spiske on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Correlation Pitfalls, Spurious Associations & Causality

Build disciplined interpretations of correlations in observational data. Explore common causes, reverse direction, shared time trends, selection, restricted ranges, nonlinear relationships and ecological inference. Prerequisites: scatter plots and Pearson and rank correlation. Original scenarios move from recognizing a plausible alternative explanation to evaluating study designs and the scope of intervention claims. Worked solutions explain why tempting conclusions exceed the evidence. Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Non-parametric & Rank Correlation

Compare monotonic and linear association through Spearman and Kendall methods. Assign average ranks, count concordant and discordant pairs, compute untied and tied examples, and assess transformation invariance and sensitivity. Prerequisites: Pearson correlation and elementary counting. Ties and zero rank variance are handled explicitly; advanced inference is deferred. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: SciPy: Spearman correlation SciPy: Kendall correlation

statistics

Oct 23, 2026

20 questions

Quiz

Pearson Product-Moment Correlation Coefficient (r)

Develop practical mastery of Pearson correlation through centered sums, covariance, standard deviations and standardized scores. Examine bounds, constant inputs, affine transformations, outliers, nonlinear structure and the lesson of Anscombe’s quartet. Prerequisites: covariance and standard deviation. The set emphasizes descriptive reasoning and reproducible calculations; formal tests and vector-geometric proofs are deferred. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: SciPy: Pearson correlation NIST: scatter plots

statistics

Oct 23, 2026

30 questions