ABSTRACT
Statistics is the solution to an inverse problem: given the outcome from a random process, the statistician infers aspects of the underlying probabilistic structure that generated the data. This chapter reviews some elementary aspects of probability, and reviews some classical tools for inference about a distribution’s location parameter. It also reviews some important elementary probability distributions, and then reviews a tool for embedding a probability distribution into a larger family that allows for the distribution to be recentered and rescaled. The distributions represent mechanisms for generating observations that might potentially be analyzed nonparametricly. Statisticians are often asked to choose among potential hypotheses about the mechanism generating a set of data. This choice is often phrased as between a null hypothesis, generally implying the absence of a potential effect, and an alternative hypothesis, generally the presence of a potential effect.
