Summer 2009

MATH 4400 – Directed study

Probabilistic Foundations of Actuarial Science

Date	Section	Assignment
May 28	Conditional probabilities. Independence. Bayes’ Theorem.	Refresh the theory on the topics on the left from your text (Devore or Hogg and Tanis). Work pbs 1-17 from the Practice for Exam P. See more practice problems on Resources page.
June 2^nd	Discrete random variables. Expected value and variance. The Binomial distribution.	Refresh the theory from your text (Devore or Hogg and Tanis). Continue working on the problems 1-30 You may now practice on problems: 28, 29, 31, 32, 41, 44, 48, 52 from Practice for Exam P. Warning: the problems are getting more difficult! See more practice problems on Resources page.
June 4^th	The Poisson distribution.	Review the theory from your text of choice. Practice problems (from Weiss handout): 5.78, 5.82, 5.84 (use only the Poisson distribution with ), 5.85, 5.147, 5.154, 5.163 (this one is among the exam problems if I remember correctly).
June 9	Continuous probability distributions: the Exponential model	Review the theory from your text of choice. Practice problems (from Practice Exam P):29, 33, 34, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 59, 62.
June 12	The moment generating function (MGF).	Read the handout given in class for the MGF. I am afraid there are not many problems I can assign from there: see 11.1, 11.3, 11.4. Work more of the above problems.
June 19	Transformations of random variables	See notes on Transformations of random variables See more examples worked in class. Practice problems (from practice Exam P): 71-76.
June 23	The Normal distribution.
June 25	Linear combinations of independent normal variables.
June 30	Joint probability distributions: the continuous case	Practice exam: 77, 78 (just the same), 79 (again similar), 88, 89, 90, 91, 92, 93, 94. Hogg and Tanis: 5.1.1, 5.1.2, 5.1.3-5.1.11; 5.2.1, 5.2.2, 5.2.7, 5.2.10.