Math 300 , Spring 2004, F Day 9 Hit reload to get most current version

Buffon needle data
Ash Ch.2, continued.
Bayes' theorem:  Don't memorize the theorem, just know the process.bayes tree
From knowing an outcome W, find the probability of an antecedent S.
       P(S | W) when W|S is the direction you have information for.
These can always be modeled effectively with a tree, S on the first branching, W on the second:
    Find the probability of the outcome W by summing the "fav" tree path results. (Ash's "total probability" p. 58)
    Note the probability of (S and W): just the single path with S followed by W.
    Divide: (SandW path) / (sum of W paths)
              = P(S and W)/P(W) = P(S|W)

Handout Death penalty (#3)

Reading :   Bayes' theorem,  Ash pp 58-61, M&M4th ed. pp 349-50.   Handout case study: testing for AIDS.
      ahead? Independence, M&M pp. 294-296, 340 Rule 5, 350.  Ash pp. 41-43

HW  Draw trees.  Make a table if you think it adds to your understanding.
Not Bayes, but interesting and useful:
--Moore&McCabe p. 369 4.124  Do this problem with x as the actual proportion  of plagiarism, y as the proportion who answer No.  Solve for x in terms of y.
p. 358, 4.110 (surgery or med management)  Note, the tree is only for finding P(A) under the surgery choice.

--Handout:  If not completed in class: "#2" (lefthanded families).  Make a tree and a table, with all probabilities.
--Moore&McCabe, (With p.356ff  4.101, 4.102 ) now  4.103 and 104 Bayes' th. 
  p. 362,  4.125, 126 (& read Handout--the probabilities are different--the tests have improved.  The issues are the same.)
  Optional:  p. 357, 4.105-109 are very interesting. Read the problems for the flavor, at least.

--Ash sec. 2-1, p. 44
   Add to   3a from last time: 3b.
    4, 6

Sievers home  Math300-Sp04/Dayp9.htm  8pm 2/18/04
This page belongs to Sally Sievers who is solely responsible for its content. Please see our statement of responsibility.