Mathematics 231-04   Probability   Spring 2008

Exam 3 Topics     April  23, 2008

The examination will cover  Chapters 5 and 6 from our text (and one topic from Chapter 4), as indicated below.

From Chapter 5. (Sections 5.1, 5.2, 5.4.1, 5.7)

• On a bounded interval, find C so that f is a probability density function, and then calculate the probability that X satisfies a certain inequality. (20%)
• Given a PDF on an unbounded interval, calculate a probability and determine the CDF. (20%)
• Given a PDF, find the expected value of the random variable. (10%)
• Find a normal approximation to a binomial probability. (15%)
• Find the CDF of Y = h(X), expressed in terms of the PDF of X, in a case where h doesn’t have an inverse function. (15%)

From Chapter 6. (Sections 6.3, 6.7)

• Recognize the PDF of the sum of two independent continuous random variables. (5 %)
• Find the joint PDF of (U, V) = (g(X, Y), h(X, Y)) and determine the region where it is non-zero. (15%)

The exam will not include anything about the Gamma function or Gamma random variables, Chi-squares, the Cauchy distribution, or the Beta densities. (It would have been nice to include problems about these major examples of continuous r.v.s but there wasn’t room to put them on the exam.) There will be no definitions or proofs to write. One of the problems on the test can be “done” by quoting the result of an example from the text. I don’t want the students to do it that way; instead, work the problem out from scratch.

For a sample exam use this link .