Math 300 , Spring 2008, Mon. Jan. 28, Day 1 Hit
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Reading: Ash, Intro and Sec. 1-1.
Please read Ahead,
Sec. 1-2&3
(Review: Moore & McCabe,
4.2. (for day 1, to independence , p.294 4th ed., p. 266 5th ed.)
HW: A)
Ash, p. 6, #3 thru 9 (give answers and
draw sets of outcomes on handout for 2 dice)
B) Find the probability distribution
of the sum of the 2 dice (i.e. for every possible value that the sum
can
take on, give its probability.) Arrange the values in a table
sum | 2
3
4 ...
12
Prob |
In class: Go over syllabus. Please return Questionnaire as soon as you can.
Notes are a brief overview of the material, not a
substitute for the book. Notes may also include things not in the
book.
Chance Experiment: Sample space S, events A, probability P(A).
Probability Axioms: Simple: S, P(A), probability of
events A assigned for every A
0< P(A) < 1; P(S)=1
P(Not A) = 1-P(A) (Not A
is the complement of A; all the outcomes Not described by A. Ac
or A with a bar.)
Discrete space: P(A) = sum of probabilities of all
outcomes in A
Equally likely space: P(A) = (# of outcomes favorable to A) /(total #
of outcomes)
Axioms (mathematical model: mid 20th century) common
to all Interpretations (applied to "real world")
1) "Classical" = n
"equally likely outcomes", prob of each is 1/n. (Get a lot of
mileage from this.)
but many situations don't have equally likely outcomes
2) "Frequentist"
= "empirical" , P(A) = proportion (relative frequency) of times A would
occur in a very long series of repetitions of the experiment.
but
many experiments can't be repeated a very many times...
3) "Subjective" =
"personal" = "Bayesian", P(A) is MY assignment. (Betting on
the horses. Stockmarket.)
If you have a lot of data (i.e. enough for the
Frequentist) then for a particular experiment, all of the
interpretations will give about the same probability distribution
(Bayesians are not stupid; will use evidence.) .
We'll use the Classical method to build a lot of probability models;
our underlying philosophy is Frequentist. We'll learn "Bayes'
Theorem" which Bayesians use to alter personal probabilities when they
get new evidence.
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