Standard syllabus
Probability · Undergraduate · Math
Topics
Probability foundations
- Sample spaces, events, and axioms of probability
- Combinatorial probability: permutations and combinations
- Conditional probability and independence
- Bayes' theorem and law of total probability
Random variables
- Random variables: discrete and continuous
- Probability mass functions and probability density functions
- Expected value, variance, and standard deviation
- Joint distributions; marginal and conditional distributions
- Covariance and correlation
Common distributions and limit theorems
- Common discrete distributions: Bernoulli, binomial, geometric, Poisson
- Common continuous distributions: uniform, exponential, normal
- Central Limit Theorem (statement) and normal approximations
- Sampling distributions (introduction for statistics follow-on)
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