Stat 321  Fall 2004  Exam 1 Preparation

  • Tuesday, October 5, 1:10-2:00
  • Covers chapter 2, handouts from days 1-8, investigations 1-6, suggested homework problems from weeks 1-2
  • You may use book, handouts, one other sheet of notes
  • Technology
    • Bring calculator
    • No use of Minitab
    • Minitab and/or applet output may be included
  • Interpretations, explanations as important as calculations
  • Comparable to in-class, investigation, homework questions

Big Ideas

  • Probability
    • Interpretation: long-term relative frequency
    • Approximation by simulation
      • Physical simulations
      • Java applets
    • Sample space, events
    • Equal likeliness
      • Counting rules
        • General multiplication rule
        • Permutations
        • Combinations
    • Basic probability rules
      • Complement rule
      • Addition rules
    • Conditional probability
      • Definition
      • Interpretation
      • Multiplication rule
      • Law of total probability
      • Bayes’ Theorem
      • Independence
  • Statistical tests
    • Logic, reasoning, p-value
      • Empirical approximation via simulation
      • Exact calculation
    • Fisher’s exact test
      • Hypergeometric distribution

Some Advice

  • Be prepared to think/explain/interpret
    • Do not just plug into formulas from text
  • Organize note sheet for efficient retrieval of information
  • Don’t plan to use text, handouts too much
    • Prepare as if exam were closed book/notes
    • Understand, don’t memorize
    • Time may be a concern
  • Re-read
    • Handouts
      • Especially expository passages, “boxed” paragraphs
    • Chapter from text
  • Review problems
    • Re-work examples from handouts
    • Re-work investigations
    • Work suggested homework problems
    • Re-work examples from text
    • Work additional exercises from text

Problem-Solving Strategies

  • Process
    • Clearly identify and define events
    • Record given information with appropriate symbols
    • Identify what’s asked for with appropriate symbols
    • Decide what rules apply
      • And/or construct probability tables or trees
  • Probability rules
    • Translations
      • “or” is union (addition rule)
      • “and” is intersection (multiplication rule)
      • “not” is complement (complement rule)
    • Counting
      • If order matters: permutations
      • If order does not matter: combinations
      • Be sure to count the same way in numerator and denominator
    • If event of interest is hard, try its complement
      • P(at least one) = 1-P(none)
    • Venn diagrams, tables and trees can be helpful
    • Check for independence before applying general multiplication rule
    • Conditional probabilities
      • Multiplication rule: looking for probability of intersection and know conditional probability
      • Total probability: looking for unconditional probability and know conditional ones
      • Bayes’ theorem: looking for “reverse” conditional probability