1. Converting an experiment with a random outcome to a random variable and choosing an appropriate probability distribution.
2. Basic probability calculations in standard discrete and continuous distributions, including distributions such as the gamma and beta which require skill at handling two parameters.
3. Computation of expected values and variances in a variety of distributions.
4. Joint and marginal distributions, conditional distributions, covariance, independence.

In the first part of Math Stat I, in our review of probability, we will focus on more advanced probability topics, such as distributions of functions of random variables (including functions of multiple random variables), families of distributions such as exponential families and location-scale families, the use of moment-generating functions, hierarchical models, and the multivariate normal distribution. In the homework problems on these more advanced topics, students will have multiple opportunities to demonstrate their understanding of the more basic probability techniques as well.