The first midterm is on Wednesday, March 5, during the regular class period.
The following is a chapter by chapter guide intended to help you organize the material we have covered in class as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study. It is also important you are comfortable with material from previous pre-requisite classes.
Please review all homework and quiz problems for the chapters given below, as well as examples worked out in class and in the textbook. You are also encouraged to work out the "self-test problems and exercises" at the end of each section for more practice. In addition, Prof. Eugene Speer has an excellent collection of review problems on his website.
1: This chapter covers many different counting techniques. All of the definitions, equations and examples in this chapter are very important. Pay careful attention to whether the things you are counting consist of ordered or unordered arrangements.
2: You should know how to clearly and precisely describe the sample space of an experiment, and how to describe events as a subset of this sample space. You should feel comfortable with all the set operations described in this chapter, and you are welcome to use Venn diagrams whenever it is convenient. You should be able to state the axioms of probability. Finally, you should be able to calculate the probabilities of events in a sample space where each outcome is equally likely to occur, using the methods of Section 2.5. Note that Sections 2.6 and 2.7 were not covered and will not be included on exams.
3: Know how to compute conditional probabilities using the definition of Equation 2.1 in Section 3.2. Furthermore, you should be able to expand out the terms in equation using the multiplication rule, which gives you Bayes's Formula. You should understand what it means for 2 or more events to be independent, and what it means to be conditionally independent.
4: Make sure you understand what a random variable, especially a discrete random variable. For such a variable, you should be able to find the probability mass function, cumulative density function, expected value, variance and standard deviation. You should also know the special cases of geometric random variables, binomial random variables and Poisson random variables. You will be given the probability mass functions for these 3 special cases, but you are required to know when it is appropriate to use them. Note that Sections 4.8.2-4.8.4 and were not covered and will not be included on any exams. Also, we have not yet covered Sections 4.9-4.10, so they will not be included on this exam, but we will cover these sections for the next exam.
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