All atlases/Probability and Statistics

Mathematics Atlas

Probability and Statistics

A first course in probability and statistical inference for students with a calculus background. We move from probability models, random variables and sampling distributions to practical data-analysis: estimation, confidence intervals, hypothesis tests and regression. Emphasis is on building transferable conceptual understanding, computational skills in R, and the ability to interpret statistical evidence in real-world settings.

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Next: Foundations: Sets, Events and Axioms

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From Counting to Probability

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current pathprerequisite
Foundations: Sets, Events and Axioms appears earlier in the syllabus and supports Expectation, Variance & Moments.Expectation, Variance & Moments appears earlier in the syllabus and supports Poisson Process and Distribution.Poisson Process and Distribution appears earlier in the syllabus and supports PDFs, CDFs and Quantiles.PDFs, CDFs and Quantiles appears earlier in the syllabus and supports Normal Distribution and Standardization.Normal Distribution and Standardization appears earlier in the syllabus and supports Point Estimation and Bias.Point Estimation and Bias appears earlier in the syllabus and supports z-Intervals with Known σ.z-Intervals with Known σ appears earlier in the syllabus and supports Null and Alternative Hypotheses.Null and Alternative Hypotheses appears earlier in the syllabus and supports Two-Sample t-Test and Interval.Two-Sample t-Test and Interval appears earlier in the syllabus and supports Fitting a Line by Least Squares.prerequisite

prerequisite relationship

Foundations: Sets, Events and Axioms -> Expectation, Variance & Moments

Foundations: Sets, Events and Axioms appears earlier in the syllabus and supports Expectation, Variance & Moments.

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Foundations: Sets, Events and Axioms

Introduce the language of probability—sample spaces, events, axioms—and derive elementary rules such as the complement and inclusion-exclusion laws.

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Foundations: Sets, Events and Axioms: the core idea

Introduce the language of probability—sample spaces, events, axioms—and derive elementary rules such as the complement and inclusion-exclusion laws. The key thing to notice is: Sample space Ω as the set of all possible outcomes. A useful example is Power-ball ticket: probability of matching at least one ‘power-ball’ number using complement rule. Do not treat this as a vocabulary item; the point is to use it to reason about a new situation.

Where would Foundations: Sets, Events and Axioms show up in an everyday decision or news headline?

Look for the hidden relationship in the example: Power-ball ticket: probability of matching at least one ‘power-ball’ number using complement rule.

Foundations: Sets, Events and Axioms: the core idea