Introduction | Sample space and events | Axioms of probability | Basic theorems | Continuity of probability function | Probabilities of 0 and 1
Section 1.2: B.30, B.33, B.34
Section 1.4: A.24, B.40, B.42, B.45
Introduction | Counting principle | Permutations | Combinations | Stirling formula
Section 2.2: B.30, B.36
Section 2.3: A.29, B.34
Section 2.4: A.47, B.51, B.66
Conditional probability | The multiplicative rule | Law of total probability | Bayes' formula | Independence
Section 3.1: A.18, B.22, B.23
Section 3.2: A.10, B.13, B.14
Section 3.3: A.14, B.21, B.24
Section 3.4: A.18, B.24
Section 3.5: A.24, B.44, B.49, B.50
Sections 1.1-1.6, 2.1-2.4, and 3.1-3.5
Random variables | Distribution functions | Discrete random variables | Expectations of discrete random variables | Variances and moments of discrete random variables | Standardized random variables
Section 4.2: A.9, A.11, B.17, B.18
Section 4.3: A.6, B.14, B.17
Section 4.4: A.12, A.17, B.21
Section 4.5: A.9, A.10, A.11
Bernoulli and binomial random variables | Poisson random variables | Other discrete random variables
Section 5.1: A.23, A.25, B.32, B.33
Section 5.2: B.29, B.31, B.33, B.34
Section 5.3: A.9, A.14, B.28, B.29
Probability density function | Density of a function of a random variable | Expectations and variances
Section 6.1: 9, 12, 13
Section 6.2: A.6, A.7, B.9
Section 6.3: A.10, B.14, B.18, B.19
Section 7.1: A.9, B.12, B.15, B.17
Chapter 4, 5 (not including hypergeometric random variables), 6 and Section 7.1
Uniform random variable | Normal random variable | Exponential random variable | Gamma distribution
Section 7.2: A.23, A.24, B.29, B.30
Section 7.3: A.3, A.6, B.16
Section 7.4: A.6, A.9
Joint distributions of two random variables | Independent random variables | Conditional distributions
Section 8.1: B.29, B.32, B.34
Section 8.2: A.23, B.29, B.30
Section 8.3: A.13, A.15, B.22
Expected values of sums of random variables | Covariance | Correlation | Conditioning on random variables
Section 10.1: A.8, B.10, B.11, B.17
Section 10.2: B.18, B.20
Section 10.3: A.5, A.6
Section 10.4: A.16, A.17, B.19, B.24
Moment-generating functions | Sums of independent random variables
Section 11.1: A.18, B.22, B.24
Section 11.2: A.7, A.16, B.20
Sections 7.2-7.4, 8.1-8.3, 10.1-10.4 and 11.1-11.2