Course Description

The content of MATH 220 is divided into two related components, probability and statistics, with about 2/3 of the class devoted to the former and 1/3 to the latter. Probability theory is the science of determining the likelihood of a certain event (e.g. what is the probability of getting a royal flush in poker?)  We will first learn some fundamental concepts, such as conditional probability and independent events, and theorems, such as Bayes' Theorem, and this will requires us to develop the ability to carefully enumerate possibilities.  Next we will study some common probability distributions, such as the Poisson distribution, which governs phenomena as diverse as the arrival rate of spam email and the flux of cosmic rays through the atmosphere. In the Central Limit Theorem, we will see how probability distributions are related to the normal distribution, which describes things like measurement errors in astronomical (and other) data, particle velocities in an ideal gas, standardized test scores, and the logarithm of stock market price variations. One important skill here will be to learn how to figure out which probability distribution is appropriate in given circumstances.

After discussing probability, we will turn our attention to statistics. Whereas the former asks us to determine the likelihood of an outcome based on an assumed model of a given random process, statistics asks us to determine a reasonable model for a random process based on observed outcomes of that process. For instance, if we roll a pair of fair dice, probability theory tells us that it is six times more likely that we would see a total of 7 on the dice than that we would see a total of 12. If, on the other hand, we are given two dice and roll them 100 times, and we find that we get a total of 12 for 50 of those rolls, then we can reasonably infer that the dice are nor fair (and given more information, we could describe more explicitly the bias in the dice). We will cover a handful of statistical topics: sampling, estimation, confidence intervals, and hypothesis testing.