Probability

1. Counting and axioms

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   Set up a sample space, use counting when it helps, and apply the axioms including complements and unions.

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2. Conditional probability

   After Counting and axioms — test out to unlock

   Use the definition, Bayes, and independence on a two-stage problem without mixing them.

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3. Discrete random variables

   After Conditional probability — test out to unlock

   Work Bernoulli, binomial, and geometric, including PMF, CDF, and a simple expectation.

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4. Continuous random variables

   After Discrete random variables — test out to unlock

   Use a PDF and CDF for uniform and exponential, and compute a probability as an integral.

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5. Expectation and variance

   After Continuous random variables — test out to unlock

   Compute E and Var, including linearity, and use them on a sum of independent variables.

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6. Limit theorems

   After Expectation and variance — test out to unlock

   State LLN and CLT in a form you can use, and apply a normal approximation with a check that n is large enough.

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Why a path, not a playlist

Axioms, conditionals, random variables, limits. Later headings open after the one before.

Each heading is its own course with a tutor. Later headings open when you finish — or test out of — the one before.

After you sign in

• •You land on this map — every heading is already there.
• •Take the open class, or test out of a later heading to unlock it.
• •Each heading is one shared course — same syllabus and first class for everyone. Later classes continue on your copy.