Standard syllabus
Probability · Undergraduate · Statistics
Topics
Probability foundations
- Sample spaces, events, and axioms of probability
- Combinatorial counting: permutations and combinations
- Conditional probability and independence
- Bayes' theorem and law of total probability
Random variables and distributions
- Discrete and continuous random variables
- PMFs, PDFs, and CDFs
- Expected value, variance, and moment generating functions (intro)
- Joint, marginal, and conditional distributions
- Covariance and correlation
- Common discrete distributions: Bernoulli, binomial, geometric, Poisson
- Common continuous distributions: uniform, exponential, normal
Limit theorems
- Law of large numbers (statement)
- Central limit theorem and normal approximations
- Chebyshev's inequality (optional)
- Applications to sampling and estimation preview
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