Math 300 , Spring 2004, M Day 7 After class
Class was spent reviewing HW questions, with handout.
I didn't get to Sec 1.5, p.34, #1c or 6, but will next time.
HW for
Day 7: Run Buffon needle simulation
as on handout, bring in results so we can see how good estimations
of pi are.
Soon (Wed or Fri) I will give out a mini-exam
(open book takehome, 2 class-days to complete) on the material covered
thru Ash's Ch. 1.
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Next:
There are 3 ways of connecting probability theory as mathematics
with the real world.
Classical = equally likely =, "model based"
Relative frequency = "frequentist"
Subjective = "Bayesian"
HW Read pp. 139-148 in Wild
& Seber, Chance Encounters (outside my door).
On the handout (xerox of p. 148, your copies in the book),
Read the quiz questions and answer mentally, and Do exercises 1, 2, 3,
using the work in that chapter .
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Ash Ch.2.We'll use Moore&McCabe 4th ed. section 4.5 with
Ash 2.1(conditional prob. and independence) &2.4 (sequences and Bayes'),
review section 5.1 with Ash 2.2 (Binomial, multinomial)
Most of Ash's examples stay with the "equally likely" model of
probability, but often the work extends to the other models as well.
Conditional probability and chain rules:
3 presentations: Venn diagram, two-way table
(both good for two "things"), tree (especially good for causal
or decision sequence; can work for sequence of 2, 3, or more things).
Reading (easiest mentally): Ash 2-1, read to bottom of
p. 39 (def. of cond. prob),
Moore&McCabe , pp.343-349 (conditional probability,
chain rule, tree diagrams)
Ash, Chain rules for AND, pp. 39-41, then "Theorem of Total
probability" pp.57-8 (stop before Bayes' for now)
Moore&McCabe, Decision Analysis, pp. 350-352.
The following will be assigned next time.
HW Draw trees whenever possible
or appropriate; two-way table or Venn diagram if that is most appropriate.
(When reasonable, try to represent the problem 2 or more ways.
Moore&McCabe 4th, p. 354 ff: 4.92, 4.100,
4.111.
On separate paper (and keep) 4.101, 4.102
(I'll assign 4.103 and 104 with Bayes' th.)
Handout (back of Wild&Seber):
Old M&M 4.95 (this is an example of the Geometric distribution,
which we'll meet later.)
Ash sec. 2-1, p. 44
1, 2, 3,
4 (this is a workout of all our techniques at once)
6 Draw a picture, use geometry.
Sec 2-4, p. 61 (trees)
9
1, 2,
7
Separate paper, keep: 3a
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