1. The mode of $X \sim \text{Gamma}(\alpha, \beta)$ is $\frac{\alpha-1}{\beta}$. 2. The mode of $X \sim \text{Beta}(3, 6)$ is $\frac{2}{7}$. 3. The mode of $X \sim \text{Ber}(p)$ is $1$ if $p>0.5$, $0$ if $p<0.5$, and both $0, 1$ if $p=0.5$. 4. The mode of $p_{X|Y}$ is the MAP estimate, an extension of the ML heuristic that includes priors. 5. The median of $X \sim \text{Exp}(\lambda)$ is $\frac{\ln(2)}{\lambda}$. 6. For a Pareto distribution with PDF $f(x)=2/x^3$ for $x \ge 1$, the mean is 2, the variance is infinite, and the median is $\sqrt{2}$. 7. The median of the mixed random variable is $\ln(1.2)$.