8/30/2023

See Collector.pdf on our Google Drive folder for copies of discussion from last class.

Chapter 1 First Principles

• Multiplication Principle
  • Application 1 - Rolling Dice
  • Application 2 - Tossing a Coin k times
• Random Experiment, Sample Space, Event
• Interpretations of Probability
  • Logical
  • Relative Frequency
  • Subjective
• Probability function
• Addition rule for mutually exlusive events
• How would you prove the addition rule for an arbitrary number of events?
• Properties of Probabilities
  • If A implies B, then P(A)<=P(B)
  • Complement rule
  • General additon rule
• Equally likely outcomes
• Counting
  • Permutations
  • Combinations
    • Example 1 - In how many ways can I arrange 8 students into 8 chairs?
    • Example 2 - In how many ways can I put 8 students into 3 chairs?
    • Example 3 - Suppose there are 4 women and 4 men and I am interested in filling the three chairs in the following way: Woman-Man-Woman. In how many ways can I do this?
    • Example 4 - How many permutations exist for the letters in the word statistics?
    • Example 5 - Consider a bowl which contains 6 ping pong balls numbered 1, 2, 3, 4, 5, and 6. If we sample 3 balls without replacement,
      • how many sequences of outcomes are possible?
      • What is the probability that the first ball is a 2?
      • What is the probability that the first ball is i (for i=1, 2, ..., 6)?
      • What is the probability that the second ball is i (for i = 1, 2, ..., 6)?
    • Example 6 - A personnel officer has available 8 candidates, five men and three women, to fill 4 positions. If every combination of candidates is equally likely to be chosen, what is the probability that no women will be hired?
    • Example 7 - How many committees are possible from a group of five individuals when the size of the committee is unspecified
• Algebra of Sets
  • Properties of Set Unions and Intersections
  • Element Proofs
• Binomial Coefficient
• Binomial Theorem
• Monte Carlo Simulation
  • Simulate a trial
  • Determine success
  • Repeat the process and find the proportion of successes

Please complete your reading of Chapter 1 for Friday. Our first Problem Session will be on Friday