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Probability Theory

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

Section 10p1_10p2_Inequalities_LawOfLargeNumbers

Section 10p3_CentralLimitTheorem

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