1. Poisson and binomial distributions applied to fault occurrence in cloth rolls and expected profit from defect-based pricing. 2. Piecewise probability density function with calculation of constant, expectation, and interquartile range. 3. Binomial distribution and hypothesis testing using normal approximation for germination and growth rates in sunflower seeds. 4. Binomial and normal approximation in task completion time, solving probability inequalities for given cumulative values. 5. Cumulative distribution function analysis, calculating probabilities and conditional probabilities from piecewise definitions. 6. Discrete distribution modeling from sampling with replacement, solving for unknown ratio and deriving distribution of range. 7. Uniform distribution applications in transformations, expectations, and geometric probability involving randomly cut wires.