2021 March 10,

Math 240: Exam C Practice

Carleton College, Joshua R. Davis

Exam C is officially scheduled for this Saturday at 8:30 AM. To give you flexibility, I do not require you to take the exam at that time. Instead, we follow our usual procedure. The exam is available from Saturday 8:30 AM to Sunday 8:30 AM. During that 24-hour period, you may take the exam in any two-hour window. My intent is for the exam to take 70 minutes; the extra 50 minutes are for stress reduction, technical mishaps, etc.

This Thursday and Friday I have office hours 12:00-2:30. If those times don't work for you — for example, because you're in a distant time zone — then feel free to e-mail me for an appointment.

The exam is cumulative but focused on material that was not covered on earlier exams. To study, I recommend that you march through our textbook (or a different textbook) doing problems. Reading the book and reading your notes are also valuable, but they tend to be passive rather than active, so focus on problems. Here are a few suggestions.

  1. Let F be any CDF. In class we have discussed the inverse transform method of generating values of a random variable Y with this CDF. Prove that the method works. That is, prove that FY(y) = F(y) for all y. (Hint: Start computing in our usual manner: FY(y) = P(Y ≤ y) = ....)
  2. Section 10.7 Exercise 25 (CLT)
  3. Section 8.9 Exercise 20 (convolution)
  4. Section 6.10 Exercise 17 (MGFs and CLT)
  5. Section 7.8 Exercise 39 (covariance)
  6. Section 9.9 Exercise 15 (conditional expectation). This problem is hard. Consider breaking it into two parts. First, if you knew the conditional density of X1 given X, then how would you solve the rest of the problem? Second, how do you compute that conditional density?