1. Continuous Distribution and Normal Approximation: Mean of waiting time using integration, probability over interval, binomial approximation to normal for large sample. 2. Uniform Distribution: Probabilities related to distances from origin, cumulative distribution sketch, and analysis of multiple independent trials with conditions on distances. 3. Binomial Hypothesis Tests: One-tailed test for decreased defect rate and two-tailed test using normal approximation for change in mean weight of pears. 4. Piecewise Probability Density Function: Determining constants, calculating probabilities, and defining full cumulative distribution function for a segmented PDF. 5. Sampling Distributions: Calculation of expected value and variance of a binomial count based on hypergeometric sampling, enumeration and probability distribution of median values from repeated sampling.