Chapter 1. Descriptive statistics

• Course overview
• Population, sample, variable
• Four levels of measurement
• Graphical integrity
• Measures of location
• Measure of variability
• Data visualization

Chapter 2. Probability

• Sample space, events
• Set operations
• Probability axioms
• Product rule
• Permutation
• Combination
• Conditional probability
• Multiplication rule
• Total probability theorem
• Bayes' rule
• Independence

Chapter 3. Discrete random variables

• Random variables
• Probability mass function (PMF)
• Cumulative distribution function (CDF)
• Expected value
• Variance
• Discrete uniform distribution
• Bernoulli distribution
• Binomial distribution
• Geometric distribution

Chapter 4. Continuous random variables

• Probability density functions (PDF)
• Continuous CDF
• Continuous expectation & variance
• Uniform distribution
• Exponential distribution
• Normal distribution

Chapter 5. Joint random variables

• Joint & marginal PMF
• Conditional PMF
• Discrete independence
• Joint PDF
• Marginal PDF
• Conditional PDF
• Continuous independence
• Joint expectation
• Covariance & correlation

Chapter 6. Limit Theorems

• Chebyshev inequality
• Law of large numbers
• Central limit theorem

Chapter 7. Point & interval estimations

• Maximum likelihood estimate
• Confidence interval

Chapter 8. Hypothesis testing

• Hypothesis test
• p-value
• z-test
• t-test
• Proportion test
• Two-sample z-test
• Two-sample t-test