SM230 - Final Exam Topics

J. Turner

Last Revision 4/22/97

This document is for public distribution

Materials: At a minimum, all students will be allowed to use calculators.

Individual instructors may also supply additional formulas and/or tables, at their discretion.

Students should check with their own instructor for the "final" say.

  1. Venn diagrams. Given P(A), P(B), P(AUB) or P(A&B), find P(Ac & Bc).
  2. Conditional probability. Calculate P(A|B) given P(A), P(B) and P(A&B).
  3. Bayes Thm. Calculate P(A) given P(A|B), P(B) and P(A | Bc), P(Bc).
  4. Given (or calculated) P(A|B) and P(A), are A and B independent? If not, are they positively correlated or negatively correlated?
  5. Bayesian search, "simple" and single sector.
  6. Monty Hall.
  7. Given arbitrary F(x), calculate probabilities of intervals.
  8. Calculate probabilities using BCDF, HCDF, PCDF. Where feasible, the story should suggest the appropriate model. The calculations include P(X=k) as well as P(X<=k).
  9. Given PMF p(x), p(y) for discrete RVs (either given in a table or given by name), calculate P(X+Y=k).
  10. Find probabilities for normal random variables.
  11. Normal approximation to binomial cdf. Central Limit Theorem applied to averages and sums.
  12. Calculate probabilities for uniform RV. Also, apply Central Limit Theorem to sums of uniforms.
  13. Given the cdf F(x) for continuous RV and Y=h(X), find cdf for Y. Find E(Y) and StdDev(Y).