Tues Sep 16 - Statistics Lecture Notes

• questions
• Go over homework
• Talk about how to use Mathematica;
  see my MathematicaStatsPrimer notes.
• Long winded dice example;
  see my Dice Statistics notes.
• Talk about using Mathematica.
• chapter 3
  • bar graphs - comparing things; any (numeric) units on Y
  • histogram - *counting* things; plots *numbers* on Y
  • stem and leaf plot : poor man's histogram
  • "size of the bin" can change histogram appearence, as well as units and scale.
• chapter 4 - intro probability
  • definition
  • AND - multiply; OR - add. Discuss.
  • Since probabilities add to 1, P(not X) = 1 - P(X) for any X.
  • Do example 4.7 in text.
  • probability distributions vs histograms : same but for normalization
  • formally: "random variables"
• depending on time - appendix C - conditional probability
  • Conditional probability P(A|B) = Probability of A given B.
  • Independent: A and B are independent iff P(A) = P(A|B).
• Counting and combinatorics (not in text)
  • To get probabilities, need to know "how many ways"
  • Permutations: number of ways to select N distinct objects - order matters
  • Combinations: number of ways to select M things from N objects, without caring about the order.
  • Factorial: N! = N * (N-1) * (N-2) * (N-3) * ...
• Mean (again)
  • revisit formula for mean using probabilities
  • "Expected value" - motivated by games of chance
  • Petersberg Paradox - (and brief aside to economic's notion of "utility")
• Examples
  • Given N people, what are odds that two have the same birthday?
  • What is the probability of being dealt a straight flush?
  • If you toss 5 coins, what is the probability that you'll get 2 heads and 3 tails?