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

II. Basics of Discrete Random Variables
 A.  Definition of a r.v.
   1. Discrete r.v.'s
   2. Discrete probability distributions
     a. Representations:  Table, Graph, Formula
   3. Properties of a Valid Discrete probability distribution
 B.  Expected Values
   1. Definition of expected value
     a. Interpretation as a population mean
   2. Expected Value of a function of a r.v.
     a. Expected values involving constants
     b. Expected Value of a sum of functions of a r.v.
   3. Definition of variance
     a.  Definition of standard deviation
     b.  Alternative formulation of the variance
   4. Finding expected value and variance for a given discrete probability distribution

III. Special Discrete Probability Distributions
 A.  The Binomial Distribution
  1.  Definition of a Binomial Experiment
  2.  How does a binomial r.v. relate to a binomial experiment?
  3.  Binomial probability function
  4.  Finding binomial probabilities using the probability formula
  5.  Finding (cumulative) binomial probabilities using Table 1
  6.  Mean of a Binomial r.v.
  7.  Variance and standard deviation of a Binomial r.v.
  8.  The Bernoulli distribution
 B.  The Geometric Distribution
  1.  Sampling structure for a geometric-type experiment
  2.  Geometric probability function
     a. Finding geometric probabilities using the probability formula
  3.  Using formulas for sums of geometric series
  4.  Mean of a geometric r.v.
  5.  Variance and standard deviation of a geometric r.v.
 C.  The Negative Binomial Distribution
  1.  Main difference between NB r.v. and geometric r.v.
  2.  Negative Binomial probability function
     a. Finding Negative Binomial probabilities using the probability formula
  3.  Mean of a Negative Binomial r.v.
  4.  Variance and standard deviation of a Negative Binomial r.v.
  5.  Main difference between binomial and negative binomial r.v.'s