Discrete random variables including joint distributions, marginal distributions, covariance, and correlation coefficient.
Poisson distribution Po(λ) as a model for rare events, calculating probabilities, and using mean = variance = λ.
Approximating Poisson Po(λ) to normal distribution N(λ,λ) when λ is large, with continuity correction.
Approximating binomial B(n,p) to Poisson Po(np) when n is large and p is small.
Probability generating functions for discrete distributions, finding moments and using properties.
Cumulative distribution functions F(x) = P(X ≤ x) for discrete and continuous variables, finding probabilities from CDFs.
Exponential distribution for continuous waiting times, memoryless property, and relationship to Poisson process.
Bivariate data analysis including scatter diagrams, linear correlation (Pearson's and Spearman's rank), and effect of coding.
Linear regression lines (y on x and x on y), least squares method, predictions, and effect of coding on regression.
Moment generating functions M(t) = E(e^{tX}), finding moments by differentiation, and using MGFs to identify distributions.
Linear combinations of independent normal random variables, finding distributions of sums and differences.
Distribution of sample mean X̄, Central Limit Theorem for large samples, and standard error.
Hypothesis testing for population mean μ when variance is known, using normal distribution, critical regions and p-values.
Hypothesis testing for Pearson's product-moment correlation coefficient ρ using critical values or p-values.
Hypothesis testing for Spearman's rank correlation coefficient using critical values or p-values.
Hypothesis testing for Poisson parameter λ, including one-tailed and two-tailed tests.
Gamma distribution Γ(α,β) for continuous positive random variables, properties and applications.
Chi-squared distribution for goodness of fit tests and contingency tables, degrees of freedom, and critical values.
Yates' continuity correction for chi-squared tests with 1 degree of freedom to improve approximation.
Non-parametric tests that don't assume specific population distributions.
Wilcoxon signed-rank test and Wilcoxon rank-sum test for comparing medians and distributions.