MATH-17 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Probability and Statistical Inference
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Sign in to save this learning pathPractical outcome: Model product defects and explain conditional uncertainty.
Explain sample spaces using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain probability axioms using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain conditional probability using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain independence using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain bayes' theorem using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Use the first concepts from this section. Model product defects and explain conditional uncertainty. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain random variables using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain expectation using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain variance using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain binomial distribution using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Explain normal distribution using a visual and one worked real-world example. Context: Model product defects and explain conditional uncertainty. End with a prediction or check-for-understanding.
Model product defects and explain conditional uncertainty. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Sample spaces, Probability axioms, Conditional probability and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Estimate a population mean from a reproducible sample.
Explain joint distributions using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain covariance using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain law of large numbers using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain central limit theorem using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Use the first concepts from this section. Estimate a population mean from a reproducible sample. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain sampling bias using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain point estimation using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain likelihood using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain confidence intervals using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Explain bootstrap using a visual and one worked real-world example. Context: Estimate a population mean from a reproducible sample. End with a prediction or check-for-understanding.
Estimate a population mean from a reproducible sample. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Joint distributions, Covariance, Law of large numbers and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare two process changes without confusing association and causation.
Explain null hypotheses using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain p-values using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain type i and ii errors using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain statistical power using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain multiple comparisons using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare two process changes without confusing association and causation. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain linear regression using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain residual diagnostics using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain confounding using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain randomised experiments using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Explain bayesian updating using a visual and one worked real-world example. Context: Compare two process changes without confusing association and causation. End with a prediction or check-for-understanding.
Compare two process changes without confusing association and causation. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Null hypotheses, P-values, Type I and II errors and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Compare two process changes without confusing association and causation. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Probability and Statistical Inference, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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