As professor, I prepared these PDFs as class notes for a course in probability theory. The class covered chapters in Blitzen and Hwang’s “Introduction to Probability” (Harvard). They include lecture notes and example problems which have been worked out in some detail. I hope you find these useful.
Section 1p1_1p4_SampleSpace_NaiveDefinition_Counting_OverCounting
Section 1p5_1p6_Stories_NonNaive
Section 2p1_Think_Conditionally
Section 2p2_2p3_2p4_ConditionallyProb_Bayes_LOTP
Section 2p5_2p8_Independence_Coherency_ProblemSolving_PitfallsParadoxes
Section 3p1_3p2_RandomVariables_Distributions_ProbabilityMassFunctions
Section 3p3_3p5_Bernoulli_Binomial_Hypergeometric_Uniform
Section 3p6_3p8_CumulativeDistributionFunctions_FunctionsOfRvs_Independence
Section 4p1_4p3_Expectation_Linearity_Geometric_Negative_Binomial
Section 4p5_4p6_LOTUS_Variance
Section 4p7_5p1_Poisson_ProbabilityDensityFunctions
Section 5p2_5p3_Uniform_Universality
Section 5p4_5p5_Normal_Exponential
Section 6p1_6p3_DistributionSummaries_Moments_SampleMoments
Section 6p4_MomentGeneratingFunctions
Section 7p1_7p2_JointMarginalConditional_2DLOTUS
Section 8p1_ChangeOfVariables
Section 9p1_9p2_ConditionalExpectation
Section 7p3_Covariance_Correlation