MA/CS 109 The Art and Science of Quantitative Reasoning Probability

Our primary topic for the three-week statistics module in this class will be inferential statistics. Inferential statistics is concerned with making precise quantitative statements about a population, given data on that population, while acknowledging the inherent uncertainty in the data. This uncertainty may be an unavoidable aspect of our data collection or, alternatively, may be purposely incorporated into the design of a study. In either case, in order to succeed in making precise quantitative statements we require a language and associated mathematical machinery for quantifying the uncertainty we face. For this purpose we employ probability. We will spend the first week of our module laying a modest foundation in elementary probability. Although the topic is both broad and deep, even at a foundational level, our treatment will necessarily be minimal. Our goal here will be simply to gain some basic understanding of what probabilities are, how they behave, and how to interpret them. An understanding of these issues will, in turn, greatly facilitate our discussion of select topics in inferential statistics in the second and third weeks of our module. Probability will also be seen, in a quick detour back to computer science, to be central to certain types of cryptography, where its usage is purposeful and – to any of us relying on password encryption – beneficial.