STAT 511 -- EXAM 1 REVIEW SHEET 

I.  Probability Fundamentals
 A.  Randomness and Types of Probability
  1.  Subjective Approach
  2.  Relative Frequency Approach
  3.  Axiomatic Approach
 B.  Set Notation
  1.  Sample Space
  2.  Null (empty) set
  3.  Venn Diagrams
  4.  Union and Intersection of sets
  5.  Complement of a set
  6.  Mutually exclusive sets
  7.  Laws of Set Notation
    a. Distributive Laws
    b. DeMorgan's Laws
 C.  Discrete Probability Models
  1. Experiment, Sample points, and Sample Space
  2. Definition of event
    a. Simple event
    b. Compound event
  3. Kolmogorov's 3 Probability Axioms
    a. Probability of a union of pairwise m.e. events
  4. Complement Rule and other simple probability rules
  5. Additive Law of Probability (for Union)
  6. Adding probabilities of sample points
 D. Tools for Counting Sample Points
  1. "mn" rule (and extensions to more than 2 sets)
  2. Number of permutations of n objects, taken r at a time
  3. Number of permutations of n objects when objects are not all distinct
  4. Combinations:  Number of ways to select r objects from a set of n objects
 E. Conditional Probability and independence
  1. Definition of conditional probability 
  2. Definition of independent events 
  3. Multiplicative Law of Probability
  4. Probability of an intersection of INDEPENDENT events
 F. Writing an event as a composition of simpler events
  1. Using unions, intersections, complements
  2. Using established probability rules on this composition
 G. Total Probability / Bayes' Rule
  1. Definition of a partition of S
  2. Law of Total Probability
  3. Corollary of LTP involving complements
  4. Bayes' Rule
  5. Corollary of Bayes' Rule involving complements