Review Sheet for Test II, Spring 2017
Colorado State University, Pueblo
Math 156 — Introduction to Statistics

Definitions

Terms you should know -- be able to state clearly what they mean, recognize them in examples, and create your own examples of them
  1. [repeatable] experiment
  2. sample space, outcomes, and events
  3. probability model
  4. frequentist view of probability
  5. complement [of a set]
  6. intersection [of sets]
  7. union [of sets]
  8. Venn diagram
  9. finite probability model
  10. fair coin or fair die
  11. disjoint or mutually exclusive
  12. addition rule for probabilities of disjoint events
  13. conditional probability
  14. independent [events]
  15. multiplication rule for probabilities of independent events
  16. random variable [RV]
  17. discrete and continuous [for RVs]
  18. the [probability] distribution of a discrete RV
  19. the expectation [or expected value or mean] of a discrete RV
  20. the [probability] density function of a continuous RV
  21. the uniform distribution
  22. the Normal distribution $N(\mu,\sigma)$ with mean $\mu$ and standard deviation $\sigma$
  23. the 68-95-99.7% Rule

Things to know how to do

  1. given a description of some situation with a repeatable experiment:
    1. state what is the sample space
    2. list events
    3. figure out an appropriate probability model
    4. make an appropriate and accurate Venn diagram
    5. compute probabilities and conditional probabilities of events
    6. determine if events are disjoint
    7. determine if events are independent
  2. given a description of some situation where a repeatable experiment has associated random variable
    1. figure out the distribution, if the RV is discrete
    2. figure out the expectation, if the RV is discrete
    3. figure out the density function, if the RV is continuous
    4. for any RV, figure out probabilities from its distribution or density function
  3. know when to use a uniform or Normal model for an RV, and how to compute probabilities from that model
  4. know how to compute probabilities, or values corresponding to certain probabilities, for Normal RVs, using the 68-95-99.7% Rule
  5. analyze, interpret, and critique someone else's probability computation
  6. determine if games of chance are fair, or what their long-term average or total winnings or losses would be

Format of the test

Problems will be of a level of difficulty and wording similar to those on homework and quizzes. There will also be one problem with some information to interpret as if for an ASE. The total points for the test will be well more than 100, you can choose which 100 points you want to do out of the available problems. This means you should definitely choose to do first the problems about which you are the most confident, only coming back for the rest after finishing your first pass through the entire test.

Don't forget your calculator or whatever electronic tool[s] you like and notes or books to consult. While you can consult notes, you should always do so simply to make certain you have the right formula or you are checking all of the appropriate conditions — you should know the general shape of all the formulæ, results, and definitions.

How to Study

It might be a good idea to put together all of your Big Ideas, review them, and make sure you know all of the things they describe.

Go over your quizzes, HW problems, and quizzes, and make sure you know how to do those kinds of things, and that you could do them again and get perfect scores on them now. Maybe practice writing good solutions with complete explanations and justifications of every step.

Look at your ASEs and make sure you know how you could change them so that you would get a better score (if that is possible).