MATH 314 Quiz 06

1. Provide an example of the Uniform distribution. No coins, dice, nor cards. State the values of the parameters $a,b$ that make sense in the context of your example.
2. Suppose $S = \{0, 1\}$. Which distribution over the possible outcomes of $S$ is more flexible, the Uniform or the Bernoulli? Explain your answer.
3. Consider the two datasets below. Without calculating the means or variances, compare the means and variances across the two datasets.
   1. $3, 5, 8, 13$
   2. $3, 5, 8, 20$
   1. Which dataset has the larger mean? Why?
   2. Which the larger variance? Why?
   3. What do your conclusions say about the relationship between the expectation values $\mathbb{E}[X]$ and $\mathbb{V}[X]$? Explain.