Tues Sep 16 - Statistics Lecture Notes
- 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
- 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")
- 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?
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