• Chapter 1: Introduction (1:57:03, 42 videos)
• Introduction (2:56)
• 1.1 Applications (28:33)
• Probability problems
• Monty Hall (Let's Make a Deal) problem (2:11)
• Birthday problem (4:56)
• Statistical applications
• Statistical application 1 -- Univariate data set (4:12)
• Statistical application 2 -- Bivariate data set (2:23)
• Statistical application 3 -- Bivariate data set (3:33)
• Statistical application 4 -- Multivariate data set (5:30)
• Statistical application 5 -- Regression (5:46)
• 1.2 Counting Techniques (1:11:16)
• Enumeration vs. counting (2:03)
• Multiplication rule
• Multiplication rule (2:37)
• Multiplication rule -- Example 1 (2:30)
• Multiplication rule -- Example 2 (1:44)
• Multiplication rule -- Example 3 (0:56)
• Multiplication rule -- Example 4 (2:32)
• Multiplication rule -- Example 5 (2:15)
• Multiplication rule -- Example 6 (1:14)
• Permutations
  • Permutations (3:23)
  • Permutations -- Example 1 (1:41)
  • Permutations -- Example 2 (4:06)
• Circular permutations
• Circular permutations -- Example 1 (2:58)
• Circular permutations -- Example 2 (3:10)
• Nondistinct permutations
• Nondistinct permutations (1:30)
• Nondistinct permutations -- Example 1 (0:43)
• Nondistinct permutations -- Example 2 (0:48)
• Nondistinct permutations -- Example 3 (1:36)
• Nondistinct permutations -- Example 4 (1:25)
• Combinations
• Combinations (3:10)
• Combinations -- Example 1 (1:45)
• Combinations -- Example 2 (2:17)
• Combinations -- Example 3 (2:34)
• Notes on combinations (7:33)
• Partitioning -- Example 1 (1:20)
• Partitioning -- Example 2 (2:01)
• Partitioning -- Example 3 (2:03)
• Partitioning -- Example 4 (3:05)
• Unifying Example (8:17)
• 1.3 Sets (14:18)
• Set theory definitions (2:56)
• Operations on sets (1:49)
• Venn diagrams
• Venn diagrams -- Example 1 (1:57)
• Venn diagrams -- Example 2 (2:08)
• Set theory notes (1:50)
• Set theory application (3:38)
• Chapter 2: Probability (2:41:05, 41 videos)
• Probability introduction (1:32)
• 2.1 Random Experiments, Sample Spaces & Events (11:45)
  • Random experiments (1:23)
  • Sample space examples (3:24)
  • Sample space classification (3:21)
  • Sample space subsets -- events (3:37)
• 2.2 Probability Axioms (33:09)
  • Approaches for computing probabilities (0:39)
  • Relative frequency approach to estimating probabilities (9:23)
  • Relative frequency approach to estimating probabilities -- limiting case (1:26)
  • Subective approach to estimating probabilities (3:28)
  • Classical (equally-likely) approach to calculating probabilities (4:07)
  • Probability axioms (1:55)
  • Complementary probability (2:59)
  • Probability result concerning subsets (3:03)
  • Probability of unions of events (6:09)
• 2.3 Equally-Likely Case (45:24)
  • Computing probabilities -- Example 1 (2:47)
  • Computing probabilities -- Example 2 (5:27)
  • Computing probabilities -- Example 3 (1:52)
  • Computing probabilities -- Example 4 (3:06)
  • Computing probabilities -- Example 5 (5:55)
  • Computing probabilities -- Example 6 (4:22)
  • Computing probabilities -- Example 7 (2:56)
  • Computing probabilities -- Example 8 (4:04)
  • Computing probabilities -- Example 9 (4:40)
  • Computing probabilities -- Example 10 (5:14)
  • Computing probabilities -- Example 11 (5:01)
• 2.4 Conditional Probability (23:51)
  • Conditional probability -- Example 1 (3:01)
  • Conditional probability -- Example 2 (3:16)
  • Conditional probability notes (3:58)
  • Conditional probability -- Example 3 (3:08)
  • Rule of elimination -- law of total probability (4:09)
  • Conditional probability -- Example 4 (6:19)
• 2.5 Rule of Bayes (22:48)
  • Rule of Bayes (4:17)
  • Rule of Bayes -- Example 1 (7:54)
  • Rule of Bayes -- Example 2 (10:37)
• 2.6 Independence (24:08)
  • Independence (2:10)
  • Independence -- Example 0 (2:38)
  • Independence -- Example 1 (4:22)
  • Mutual independence (1:40)
  • Independence in a series system (2:13)
  • Independence in a parallel system (2:36)
  • Mutual independence -- craps (8:29)
• Chapter 3: Random Variables (5:29:49, 93 videos)
• Random variables introduction (1:35)
• 3.1 Discrete Random Variables (45:58)
  • Discrete random variables (5:12)
  • Discrete random variables -- Example 1 (3:51)
  • Discrete random variables -- probability mass functions (4:02)
  • Discrete random variables -- Example 2 (2:48)
  • Discrete random variables -- Example 3 (3:12)
  • Discrete random variables -- Example 4 (4:24)
  • Discrete random variables -- Example 5 (4:47)
  • Discrete random variables -- Example 6 (3:39)
  • Discrete random variables -- Example 7 (5:39)
  • Discrete random variables -- Example 8 (6:12)
  • Discrete random variables summary (2:12)
• 3.2 Continuous Random Variables (29:15)
  • Continuous random variables (6:23)
  • Continuous random variables -- probability density functions (3:05)
  • Continuous random variables -- Example 0 (3:18)
  • Continuous random variables -- Example 1 (2:17)
  • Continuous random variables -- Example 2 (4:21)
  • Classifying random variables (1:42)
  • Mixed random variables (4:49)
  • Continuous random variables summary (3:20)
• 3.3 Cumulative Distribution Functions (1:47:08)
  • Cumulative distribution function definition (2:08)
  • Cumulative distribution function notes (6:08)
  • Cumulative distribution function conversion F(x) ---> f(x) (2:19)
  • Cumulative distribution functions -- Example 1 (4:01)
  • Cumulative distribution functions -- Example 2 (4:36)
  • Cumulative distribution functions -- Example 3 (2:16)
  • Cumulative distribution functions -- Example 4 (4:34)
  • Cumulative distribution functions -- Example 5 (7:29)
  • Cumulative distribution functions for mixed random variables (1:17)
  • Cumulative distribution function topics (1:07)
  • Percentiles
    • Percentiles (3:20)
    • Percentiles -- Example 1 (3:06)
    • Percentiles -- Example 2 (2:12)
    • Percentiles -- Example 3 (5:12)
  • Random Variate Generation
    • Random variate generation (5:22)
    • Random variate generation -- Example 1 (6:54)
    • Random variate generation -- Example 2 (6:17)
  • Transformations of Random Variables
    • Transformations of random variables (4:30)
    • Transformations of random variables -- Example 1 (5:38)
    • Transformations of random variables -- Example 2 (3:22)
  • Random Variables in a Computer Algebra System
    • APPL introduction (3:45)
    • APPL -- Example 1 (2:51)
    • APPL -- data structure (2:28)
    • APPL -- Example 2 (2:53)
    • APPL -- Example 3 (3:07)
    • APPL -- Example 4 (2:11)
  • Mixtures
    • Mixtures (1:44)
    • Mixtures -- Example 1 (2:54)
    • Mixture application (2:02)
    • Continuous mixtures (1:25)
• 3.4 Expected Values (2:10:56)
  • Expectation (2:12)
  • Expectation -- Example 1 (2:26)
  • Expectation -- Example 2 (2:11)
  • Expectation -- Example 3 (5:54)
  • Expectation -- Example 4 (2:49)
  • Expectation -- Example 5 (4:44)
  • Expectation -- Example 6 (5:37)
  • Expectation -- Example 7 (4:03)
  • Expectation -- Example 8 (4:45)
  • Expectation -- Example 9 (3:17)
  • Central tendency (1:59)
  • Central tendency -- Example 1 (4:52)
  • Population mode definition (2:20)
  • Population mean summary (2:04)
  • Topics in expectation (0:55)
  • Properties of expected values
    • Expected value of a constant (1:44)
    • Expected value of a constant times a random variable (1:31)
    • Expected value of a function of a random variable -- introduction (3:19)
    • Expected value of a function of a random variable (3:03)
    • Expected value of a function of a random variable -- Example 1 (5:13)
    • Expected value of a constant times a function of a random variable (1:20)
    • Expected value of the sum of functions of a random variable (1:34)
  • Moments
    • Population variance definition (2:46)
    • Notes on population variance (3:11)
    • Population variance shortcut formula (3:24)
    • Population variance -- Example 1 (3:23)
    • Population variance of aX + b (3:44)
    • Population variance of aX and b (4:40)
    • Popluation moment definition (0:57)
    • Standardized random variables (4:01)
    • Population skewness definition (3:06)
    • Population kurtosis definition (1:29)
    • Population skewness and kurtosis -- Example 1 (5:25)
  • Moment generating functions
    • Moment generating function definition (1:47)
    • Moment generating function theorem (2:51)
    • Moment generating function -- Example 1 (5:19)
    • Moment generating function -- Example 2 (4:38)
    • Characteristic functions (1:24)
  • Conditional expectation
    • Conditional expectation (10:59)
• 3.5 Inequalities (14:57)
  • Markov's inequality
    • Markov's inequality (2:16)
    • Markov's inequality -- Example 1 (2:46)
  • Chebyshev inequality
    • Chebyshev's inequality (2:39)
    • Chebyshev's inequality -- Example 1 (7:16)
• Chapter 4: Common Discrete Distributions (4:57:19, 60 videos)
• Common discrete distributions introduction (9:26)
• 4.1 Bernoulli Distribution (14:06)
  • Definition (3:39)
  • Bernoulli trials (1:29)
  • Population moments (6:24)
  • Summary (2:34)
• 4.2 Binomial Distribution (1:08:20)
  • Definition (5:12)
  • Notes (4:11)
  • Population mean (4:43)
  • Population moments (2:29)
  • Shape of the probability mass function (3:58)
  • Binomial distribution -- Example 1 (6:56)
  • Binomial distribution -- Example 2 (12:47)
  • Binomial distribution in R (1:40)
  • Binomial distribution -- Example 3 (8:41)
  • Binomial distribution -- Example 4 (7:53)
  • Binomial distribution -- Example 5 (8:14)
  • Summary (1:36)
• 4.3 Geometric Distribution (44:03)
  • Definition (4:39)
  • Existence conditions (2:43)
  • Cumulative distribution function (2:15)
  • Memoryless property (7:19)
  • Moment generating function (4:17)
  • Population mean (3:37)
  • Population moments (1:40)
  • Geometric distribution -- Example 1 (6:12)
  • Geometric distribution -- Example 1 (6:12)
  • Alternative geometric distribution (3:21)
  • Geometric distribution -- Example 2 (8:00)
• 4.4 Negative Binomial Distribution (28:22)
  • Definition (7:40)
  • Moment generating function (3:28)
  • Negative binomial distribution -- Example 1 (6:20)
  • Alternative negative binomial distribution (2:39)
  • Negative binomial distribution -- Example 2 (8:15)
• 4.5 Poisson Distribution (1:19:20)
  • Introduction (1:21)
  • Poisson approximation to the binomial distribution
    • Poisson approximation to the binomial distribution (4:52)
    • Definition (2:46)
    • Moment generating function (8:53)
    • Poisson distribution -- Example 1 (6:54)
  • Poisson processes
    • Introduction (8:34)
    • Illustrations (2:21)
    • Notation (2:39)
    • Counting processes (3:59)
    • Poisson process -- Example 1 (11:52)
    • Time between arrivals (9:48)
    • Superpositioning (2:28)
    • Decomposition (2:06)
    • Order statistics (3:13)
    • Summary (1:16)
    • Poisson process -- Example 2 (6:18)
• 4.6 Hypergeometric Distribution (18:48)
  • Introduction (2:30)
  • Definition (4:11)
  • Support (2:39)
  • Population moments (3:10)
  • Hypergeometric distribution -- Example 1 (6:18)
• 4.7 Other Distributions (29:59)
  • Discrete uniform distribution
    • Definition (6:45)
    • Discrete uniform distribution -- Example 1 (6:43)
  • Benford distribution
    • Introduction (4:43)
  • Zipf distribution
    • Introduction (4:55)
    • Zipf distribution -- Example 1 (2:48)
  • Mixture distribution
    • Mixture distribution -- Example 1 (4:05)
• Common discrete distributions summary (4:55)
• Chapter 5: Common Continuous Distributions (3:49:14, 54 videos)
• Common continuous distributions introduction (4:03)
• 5.1 Uniform Distribution (47:15)
  • Definition (4:16)
  • Cumulative distribution function (4:19)
  • Moment generating function (1:59)
  • Population moments (3:52)
  • Uniform distribution -- Example 1 (2:15)
  • Uniform distribution -- Example 2 (3:36)
  • Uniform distribution -- Example 3 (6:14)
  • Uniform distribution -- Example 4 (6:45)
  • Uniform distribution -- Example 5 (9:35)
  • Uniform distribution -- Example 6 (4:24)
• 5.2 Exponential Distribution (57:44)
  • Definition (4:26)
  • Parameter (2:35)
  • Cumulative distribution function (1:40)
  • Memoryless property (5:22)
  • Moment generating function (4:31)
  • Population moments (4:45)
  • Gamma function (4:33)
  • Exponential distribution -- Example 1 (6:27)
  • Exponential distribution -- Example 2 (5:28)
  • Exponential distribution -- Example 3 (5:40)
  • Exponential distribution -- Example 4 (9:18)
  • Summary (2:59)
• 5.3 Gamma Distribution (24:56)
  • Definition (4:49)
  • Moment generating function (3:51)
  • Population moments (1:35)
  • Special cases of the gamma distribution (5:02)
  • Gamma distribution -- Example 1 (7:31)
  • Summary (2:08)
• 5.4 Normal Distribution (45:00)
  • Introduction (7:56)
  • History (1:21)
  • Properties (10:14)
  • Normal distribution in R and APPL (1:55)
  • Moment generating function (2:43)
  • Distribution of aX + b (4:09)
  • Distribution of (X - mu) / sigma (3:28)
  • Distribution of ((X - mu) / sigma) ^ 2 (3:10)
  • Normal distribution -- Example 1 (6:29)
  • Normal distribution -- Example 2 (3:35)
• 5.5 Other Distributions (44:16)
  • Other distributions (1:00)
  • Beta distribution
    • Definition (4:39)
    • Existence conditions (2:10)
    • Population mean (2:04)
    • Population moments (0:38)
    • Beta distribution -- Example 1 (3:57)
    • Beta distribution -- Example 2 (4:20)
  • Triangular distribution
    • Definition (3:01)
    • Cumulative distribution function (3:25)
    • Population moments (1:56)
    • Triangular distribution -- Example 1 (5:19)
  • Weibull distribution
    • Definition (4:59)
    • Population moments (1:23)
    • Weibull distribution -- Example 1 (5:25)
• Common continuous distributions summary (6:00)
• Chapter 6. Joint Distributions (5:48:06, 90 videos)
• Joint distributions introduction (4:03)
• 6.1 Bivariate Distributions (1:19:11)
  • Bivariate distributions introduction (3:02)
  • Bivariate example -- Automobile data (4:04)
  • Bivariate distribution definition (1:33)
  • Bivariate probability density function (4:20)
  • Bivariate distributions -- Example 1 (5:40)
  • Bivariate distributions -- Example 2 (3:17)
  • Bivariate distributions -- Example 3 (9:09)
  • Bivariate distributions -- Example 4 (4:17)
  • Bivariate distributions -- Example 5 (4:21)
  • Bivariate distribution notation (1:39)
  • Bivariate distribution cumulative distribution function (2:18)
  • Bivariate distribution cumulative distribution function -- Example 1 (7:49)
  • Marginal distributions (2:10)
  • Bivariate marginal distributions -- Example 1 (1:41)
  • Bivariate marginal distributions -- Example 2 (5:53)
  • Bivariate marginal distributions -- Example 3 (5:15)
  • Conditional distributions (2:59)
  • Bivariate conditional distributions -Example 1 (3:27)
  • Bivariate conditional distributions -Example 2 (4:43)
  • Bivariate distributions summary (1:34)
• 6.2 Independence (31:32)
  • Independent random variables (4:00)
  • Independent random variables -- Example 1 (2:54)
  • Independent random variables -- Example 2 (5:24)
  • Independence result (2:22)
  • Independent random variables -- Example 3 (3:27)
  • Independent random variables -- Example 4 (13:25)
• 6.3 Expected Values (1:21:23)
  • Definition of Expected Value (2:29)
  • Expected values -- Example 1 (1:36)
  • Expected values -- Example 2 (6:39)
  • Expected values Theorem 1 (2:06)
  • Expected values Theorem 2 (2:45)
  • Outline of topics (0:32)
  • Covariance (4:11)
  • Covariance -- Example 1 (7:28)
  • Notes on covariance (2:47)
  • Shortcut formula for covariance (2:32)
  • Covariance -- Example 2 (10:44)
  • Covariance result 1 (3:18)
  • Covariance result 2 (4:14)
  • Correlation (2:32)
  • Correlation result 1 (0:57)
  • Correlation result 2 (4:13)
  • Correlation -- Example 1 (3:48)
  • Conditional expected values (1:20)
  • Conditional expected values -- Example 1 (3:22)
  • Conditional expected values -- Example 2 (4:56)
  • Conditional expected values -- Example 3 (3:23)
  • Notes on conditional expected values (1:41)
  • Joint moment generating functions (2:16)
  • Marginal moment generating functions (1:34)
• 6.4 Bivariate Normal Distribution (45:28)
  • Bivariate normal distribution (3:59)
  • Contours of the probability density function (4:04)
  • Correlation in the bivariate normal distribution (2:23)
  • Marginal distributions (2:05)
  • Conditional distributions (2:00)
  • Homoscedadicity (0:52)
  • Example 1 (8:42)
  • Moment generating functions (2:36)
  • Example 2 (3:05)
  • Matrix approach (7:31)
  • Example 3 (6:47)
  • Summary (1:24)
• 6.5 Multivariate Distributions (1:46:29)
  • Multivariate distributions (3:29)
  • Existence conditions (1:48)
  • Multivariate distributions -- Example 1 (4:28)
  • Multivariate distributions -- Example 2 (4:07)
  • Cumulative distribution functions (2:14)
  • Cumulative distribution functions -- Example 1 (4:31)
  • Marginal distributions -- Example 1 (3:24)
  • Conditional distributions -- Example 1 (2:13)
  • Independence (1:40)
  • Independence -- Example 1 (6:25)
  • Independence -- Example 2 (11:48)
  • Multinomial distribution (2:39)
  • Multinomial distribution -- Example 1 (3:33)
  • Expected values (1:42)
  • Expected values result 1 (1:30)
  • Expected values -- Example 1 (2:55)
  • Expected values -- Example 2 (5:08)
  • Expected values result 2 (2:42)
  • Expected values result 3 (2:49)
  • Expected values -- Example 3 (2:26)
  • Expected values -- Example 4 (6:40)
  • Expected values -- Example 5 (12:35)
  • Joint moment generating functions (1:54)
  • Multivariate distributions -- Example 1 (2:54)
  • Multivariate distributions -- Example 2 (2:43)
  • Multivariate normal distribution (2:08)
  • Multivariate normal distribution results (6:04)
• Chapter 7. Functions of Random Variables (3:21:04, 37 videos)
• Functions of random variables --- Introduction (7:17)
• Definition of a function (1:34)
• Functions -- Example 1 (3:45)
• One-to-one functions (0:49)
• Functions -- Example 2 (3:27)
• Functions -- Example 3 (1:02)
• Other types of functions (5:07)
• 7.1 Cumulative Distribution Function Technique (53:17)
  • Cumulative distribution function technique (4:51)
  • Roadmap of examples (8:03)
  • Cumulative distribution function technique -- Example 1 (5:15)
  • Cumulative distribution function technique -- Example 2 (10:37)
  • Cumulative distribution function technique -- Example 3 (12:14)
  • Cumulative distribution function technique -- Example 4 (12:17)
• 7.2 Transformation Technique (1:54:07)
  • Univariate transformation technique: Discrete case (4:41)
  • Univariate transformation technique: Discrete case -- Example 1 (7:41)
  • Univariate transformation technique: Continuous case (4:19)
  • Univariate transformation technique: Continuous case -- Example 1 (10:04)
  • Bivariate transformation technique: Discrete case (2:03)
  • Bivariate transformation technique: Discrete case -- Example 1 (14:57)
  • Bivariate transformation technique: Continuous case (2:16)
  • Bivariate transformation technique: Continuous case -- Example 1 (13:15)
  • Bivariate transformation technique: Continuous case -- Example 2 (3:10)
  • Bivariate transformation technique: Continuous case -- Example 3 (2:17)
  • Order statistics (1:59)
  • Order statistics -- Example 1 (12:36)
  • Order statistics -- Example 2 (4:50)
  • Order statistics: Joint distribution (1:59)
  • Order statistics -- Example 3 (3:00)
  • Order statistics -- Example 4 (3:08)
  • Order statistics: Marginal distributions (8:10)
  • Order statistics: Special cases (2:28)
  • Order statistics -- Example 5 (4:42)
  • Order statistics -- Example 6 (5:07)
  • Order statistics -- Example 7 (11:25)
• 7.3 Moment Generating Function Technique (10:39)
  • Moment generating function technique (4:20)
  • Moment generating function technique -- Example 1 (3:10)
  • Moment generating function technique -- Example 2 (3:09)
• Chapter 8. Limit Theorems
• 8.1 Convergence in Probability
• 8.2 Convergence in Distribution
• 8.3 Central Limit Theorem

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