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.
• 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?

Jim Mahoney (mahoney@marlboro.edu)