1. Confidence Intervals & Hypothesis Testing | Population Mean Differences & Matched-Pair Tests – Constructing a 95% confidence interval for mean height differences and performing a Wilcoxon signed-rank test for paired data.

2. Poisson Distribution & Goodness-of-Fit | Statistical Testing & Expected Frequencies – Verifying the fit of a Poisson model using a chi-square test and computing expected frequencies.

3. Probability Density Functions & Cumulative Distributions | Continuous Random Variables – Sketching and deriving the probability density function, cumulative distribution function, and median value of a given distribution.

4. Probability Generating Functions | Coin Tosses & Dice Rolls – Finding the probability generating function (PGF) for random variables representing biased coin flips and dice outcomes, and computing expected values.

5. Hypothesis Testing for Normal Distributions | Comparing Mean Wingspans of Butterflies – Conducting a t-test for two normally distributed populations with equal variances to compare mean wingspans.

6. Statistical Errors & Revisions | Impact of Data Corrections on Hypothesis Testing – Assessing whether an error in recorded data affects the conclusion of a hypothesis test.