1. Poisson and Normal Approximation: Solving problems involving Poisson distribution and applying normal approximation to calculate probabilities and assess event frequency.

2. Cumulative Distribution Functions: Deriving the probability density function, expected values, variance, and transformations involving continuous random variables.

3. Hypothesis Testing with Poisson Distribution: Constructing and evaluating critical regions, interpreting significance levels, and assessing real-world outcomes.

4. Piecewise Probability Density Function: Graphical sketching, integration for cumulative distribution, expected value analysis, and distribution skewness interpretation.

5. Binomial and Normal Approximations in Proportion Testing: Modeling binary outcomes, approximating binomial with normal distribution, and testing population proportion claims.

6. Sampling Distributions and Expectations: Defining sampling distribution, calculating the probability distribution and expected value of item totals under weighted scenarios.

7. Uniform Distribution Transformation: Analyzing transformations from area to side length, computing probabilities, and deriving variance through transformation of uniform random variables.