STAT 515 -- EXAM 1 REVIEW SHEET 

I.  Basic Fundamentals and Definitions
 A.  Types of Variables
  1.  Categorical (Qualitative)
  2.  Numerical (Quantitative)

II. Descriptive Statistical Methods for Univariate Data
 A.  Graphs and Plots
   1. Pie chart, Bar graph
   2. Stem-and-Leaf Plot, Histograms
   3. Interpreting Shapes of Histograms
   4.  Possible Advantages and Disadvantages of the Graphical Methods
 B.  (Numerical) Summary Statistics
   1. Measures of Central Tendency
     a. Sample Mean, Median
   2. Measures of Variability (Spread)
     a.  Sample Variance, Standard Deviation, Range, IQR
     b.  Box Plot and Interpreting It
   3. Shapes of Distributions
     a. Symmetric, Skewed, Bimodal

III.  Introduction to Probability
  A. Key Terms
   1. Experiment
   2. Outcome
   3. Sample Space (and Sample Points)
   4. Event
  B. Two Major Probability Properties
  C. Compound Event
   1. Unions and Intersections
   2. Understanding the meaning of each compound event
   3. Venn Diagrams
   4. Additive Rule
   5. Mutually exclusive events
   6. Conditional Probability
   7. Independent Events
      a. Intuitive definition of independent events
      b. Mathematical definition of independent events
   8. Multiplicative Rule
  D. Complement of an Event
  E. Bayes' Theorem
  F. Importance of Random Sampling

IV.  Probability Distributions for Discrete Random Variables
 A.  Random Variables
  1.  Discrete r.v.
  2.  Continuous r.v.
 B.  What Is a Probability Distribution?
  1.  Expressing a Probability Distribution through a Table
  2.  Expressing a Probability Distribution through a Formula
  3.  Expressing a Probability Distribution through a Graph
 C.  Determining the Population Mean and Variance of a Discrete r.v.
  1.  Formula for Popn. Mean mu (Expected value)
  2.  Formula for Popn. Variance sigma^2
  3.  Popn. Standard Deviation sigma
 D.  Binomial Experiments and Binomial Random Variables
  1.  What are the Characteristics of a Binomial Experiment?
  2.  What is the associated binomial random variable?
  3.  Finding Probabilities for a Binomial Random Variable
    a. Using the binomial probability formula
    b. Using Binomial Table
    c. Individual probabilities and cumulative probabilities
  4. Mean, Variance, and Standard Deviation of a Binomial Random Variable
 E.  Hypergeometric Random Variables
  1.  What are the Characteristics of a Hypergeometric random variable?
  2.  Finding Probabilities for a Hypergeometric Random Variable
    a. Using the Hypergeometric probability formula
  3. Mean of a Hypergeometric Random Variable
 F.  Poisson Random Variables
  1.  What are the Characteristics of a Poisson random variable?
  2.  Finding Probabilities for a Poisson Random Variable
    a. Using the Poisson probability formula
    b. Using Poisson Table 
    c. Individual probabilities and cumulative probabilities
  3. Mean, Variance, and Standard Deviation of a Poisson Random Variable
 G.  Expected Values and Variances of Functions of Random Variables
  1. Expected values, variances, and standard deviations of linear transformations of r.v.'s
  2. Expected values, variances, and standard deviations of sums of independent r.v.'s
  3. Expected values, variances, and standard deviations of differences of independent r.v.'s