MATH 165: Probability

Note 1 (Sec 1.1 - 1.4): Sample Space / Set Theory / Axiom of Probability (Post)

Note 2 (Sec 2.1 - 2.2): Equally Likely Outcomes / Combinatorics (Post)

Note 3 (Sec 2.3 - 2.4): Applications to Probability / The Binomial Formula (Post)

Note 4 (Sec 3.1 - 3.3): Conditional Probability  / Bayes' Formula (Post)

Note 5 (Sec 3.4 - 3.5): Independence / Probability of "At Least 1" (Post)

Note 6 (Sec 4.1 - 4.3): Discrete Random Variables / Bernoulli Distribution (Post)

Note 7 (Sec 4.3 - 4.4): Geometric and Binomial Distributions / Sampling With and Without Replacement (Post)

Note 8 (Sec 4.5 - 4.6): Expectations of Discrete Random Variables (Post)

Note 9 (Sec 5.1 - 5.4): Distribution and Density Functions / Expectation / The Uniform Distribution (Post)

Note 10 (Sec 5.5 - 5.7): The Exponential Distribution / Functions of Continuous Random Variables (Post)

Note 11 (Sec 6.1): The Poisson Distribution (Post)

Note 12 (Sec 6.2 - 6.3): The Poisson Approximation to the Binomial Distribution / The Poisson Process (Post)

Note 13 (Sec 6.4 - 6.5): Connections among Poisson, Exponential, and Uniform / The Poisson Renewal Process (Post)

Note 14 (Sec 6.5 - 8.1): The Poisson Renewal Process (continued) / The Gamma Distribution / Joint Distributions of Discrete Random Variables (Post)

Note 15 (Sec 8.2 - 8.3): Independent Discrete Random Variables / Joint Distributions of Continuous Random Variables (Post)

Note 16 (Sec 8.4 - 8.5): Independent Continuous Random Variables / The Sum of Continuous Independent Random Variables (Post)

Note 17 (Sec 8.6 - 8.9): n Independent Random Variables / Conditional Densities (Post)

Note 18 (Sec 9.1): Expectations of Functions of Random Variables (Post)

Note 19 (Sec 9.2 - 9.3): Expectations of Sums and Independent Products / The Variance (Post)

Note 20 (Sec 9.4): The Covariance and Correlation Coefficient (Post)

Note 21 (Sec 10.1 - 10.2): The Normal Distribution / Properties of Normally Distributed Random Variables (Post)

Note 22 (Sec 10.3 - 10.5): The Central Limit Theorem (Post)

Note 23 (Sec 10.6): Chebyshev's Inequality and the Law of Large Numbers (Post)

Note 24 (Sec 11.1 - 11.2): Moment Generating Functions / Proof of the Central Limit Theorem (Post)