Homework 2
Problem A Use Bayes theorem to model one of the following situations.
(i) Given a particular economic environment, news is released that updates the economic condition. How
should investors react? How would you measure overreactons?
(ii) Explai
Probability Mid-Term Exam Feb 26, 2013 Justify all reasoning.
No books, notes or calculators.
Five problems; each worth 20 points. Note second part of Problem 5 is on
second page.
1. (20 points) Recall Bayes Thm: Let B1 , ., Bn be a nite family of mutuall
Homework 1a
1.2.2 Let A, B and C be arbitrary events in the same sample space. Let D1 be the event that at least
two of the events A, B , C occur;
D2 =exactly two of the events A, B , C occur
D3 =at least of the events A, B , C occur
D4 =exactly one of th
Chapter 3 Expectations January 30, 2014
Intuitively, we would like a concept that is a "weighted average" of the possible
outcomes. In other words, we would like to give a greater weighting to more likely
outcomes. E.g., suppose an investment will return
Probability: Math 1510 January 21, 2014
Notes following Robert Ashs "Basic Probability Theory"
1. Basic Concepts.
History. Probability was originally identied with repeated experiments,
suggesting that it was closer to the physical sciences. It did not ap
Chapter 2. Random Variables. Jan 14
Let us consider first the sample space : R (reals) or a subset of the reals.
Skipping over the next step of choosing the sigma field F, we consider how we would
like to define the probability function that might describ
Homework 1b
1.5.1 Show that the events Ai , i I are independent i P (Bi1 . . . Bik ) = P (Bi1 ) . . . P (Bik ) for all
distinct i1 , . . . , ik , where each Bir may be either Air or Acr .
i
Solution.
Note that if P (Bi1 . . . Bik ) = P (Bi1 ) . . . P (Bik
PROBABILITY
CLASS REQUIREMENTS AND RULES
PROF. G. CAGINALP 507 Thackeray
Office Hours: 2 3 pm Wednesday and Friday in 507 Thackeray
Prerequisites: Math 240 (Calculus 3) and Math 420 (Introduction to the Theory of One Variable Calculus).
One or two 1000 le