Bayes rule: updating probabilities as new information is acquired. (silly) Example There are 2 coins: one is fair: P (Heads) = 1/2 one is biased: P (Heads) = 9/10 Pick one coin at random. Toss 3 times. Suppose we get 3 Heads. What then is the chance that
Balls in boxes; visual model covers many different stories. N boxes and k balls. Put each ball independently into a random box. Well study the event Ak : rst k balls all in dierent boxes.
1 P (A2) = NN 2 P (A3|A2) = NN 3 P (A4|A3) = NN . P (Ak |Ak1) = N (
Example Know a family has 2 children, and know at least one child is a girl. What is the chance the other child is a girl?
Cant answer; it depends on how we got this information.
(1) Computer list story; chance = 2/3 (2) Park story; chance = 1/2
1
The Mon
PROPORTIONS Set S = cfw_students in this room. Typical subsets A = cfw_men; B = cfw_Stat majors; C = cfw_CS majors. For any subset A write P R(A) = #A/#S. Numerical values of P R(A), P R(B), P R(C) . . . are empirical facts. But logic/arithmetic tells us
Google Aldous STAT 134 to nd course web page.
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Style of course
Blackboard and chalk (except rst 5 lectures).
We study the basic mathematics of probability . . .
. . . but its not just algebra/calculus; you need to constantly think
what the math