Information Pertaining to the 2nd Midterm Exam
Basics
The exam is an open books and open notes exam.
You can use whatever printed or written material that you bring with you
to the exam. You cannot share books or notes during the exam.
You can use a calculator and/or computer during the exam if you wish to.
(Some may wish to use software such as Maple or Mathematica, or
Wolfram Alpha.) You should not communicate with anyone about this exam.
Cell phones should be kept out of your hands while you're taking the exam.
I'll lecture for about 75 minutes, and give you about 75 minutes for the exam.
Description of the Exam
The exam has 6 problems, having a total of 10 parts. All of the parts will be weighted equally,
but I'll only count your best 9 scores from the 10 parts.
Click
here
to see the instructions for your exam.
What to Study
While some basic concepts from the first three chapters (that were covered on the first midterm exam) may be useful,
this exam will focus on Ch. 4 and Ch. 5 of the text.
Also, it'll cover just the main result from Sec. 10.1 of the text that I inserted into my coverage of Ch. 5. (So know how to transform a
uniform (0, 1) r.v. to create a r.v. having a specified continuous dist'n.)
Chapter 4
- expected value formula given near top of p. 126
- expectation formula given in Proposition4.1 on p. 129
- expression for the nth moment of a r. variable, given right before the start of Sec. 4.5 on p. 132
- definition of variance given on p. 133, and the important alternate formula given in the box near the bottom of p. 133
- Be familiar with the following families of distributions: Bernoulli, binomial, geometric, negative binomial, and hypergeometric.
Know (or be able to locate quickly) the formulas for their means, variances, and pmfs. (Keep in mind that it's an open book exam, and so you can look these things up.)
Also know the types of situations for which each distribution is commonly used. (E.g., a binomial r.v. is the number of successes in a fixed number of iid Bernoulli trials.)
Chapter 5
- obtaining probabilities using a pdf, Example on p. 5-4 of the class notes
- expected value of a cont. r. v., p. 193;
Example 2a, p. 193
- variance of a cont. r. v., p. 196;
Example 2e, pp. 196-197
- uniform distributions, pp. 197-198 (noting formulas for mean and variance given in
Example 3a, p. 198);
Example 3b, p. 199
- standard normal dist'n cdf and using it to obtain probabilities, pp. 203-205;
Example 4b, pp.204-205
- exponential distributions, pp. 211-212 (noting formulas for mean and variance given in
Example 5a, p. 212);
Example 5b, pp. 212-213
- using "cdf method" to find pdf of a function of a r.v.,
Example 7a, p. 225
- Problem 5.42, p. 231 (note that answer given in back of book isn't completely correct since the pdf isn't
1/y for all values of y ... it should be indicated that the support of the dist'n is (1, e))
- Problem 5.3, p. 234 (note that answers for the self-test problems of Ross are given in the back of the book)
Chapter 10
13 good problems to review
- Problems 5 and 8 of HW 4
- Part 4(c) of HW 5
- Parts 1(a) and 1(b) of HW 7
- Problems 1, 3, and 4 of HW 8
- Question 3 of Quiz 3
- Question 1 of Quiz 6
- Questions 1, 2, and 3 of Quiz 7
Click
here
to see the 2nd midterm exam I gave my STAT 544 class in Spring 2020.
Here
are solutions for this exam.
I suggest studying this exam in addition to the homework and quiz problems listed above.