STAT 515 Honors -- EXAM 1 REVIEW SHEET 

I.  Basic Fundamentals and Definitions
 A.  Basic Terms
  1.  Descriptive and Inferential Statistics
  2.  Individuals, Variables, Data
  3.  Population vs. Sample, Parameters vs. Statistics
  4.  Observational Study, Experiment, Survey, Published Source
 B.  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, Trimmed Mean, Mode
     b. Know how to calculate for small data sets
     c. Advantages/disadvantages for the different statistics
   2. Measures of Variability (Spread)
     a.  Why are they important?
     b.  Sample Variance, Standard Deviation, Range, IQR
     c.  Know Definitions for Each
     d.  Possible advantages/disadvantages
     e.  Box Plot and Interpreting It
   4. Determining Outliers
     a.  Method using IQR
     b.  Z-score method
   5. Shapes of Distributions
     a. Symmetric, Skewed, Bimodal
     b. Assessing whether a distribution might be normal
  C. Empirical Rule and Chebyshev's Rule
   1.  What can we conclude for them?
   2.  When does each one apply?


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 Table II in Appendix A
    c. Individual probabilities and cumulative probabilities
  4. Mean, Variance, and Standard Deviation of a Binomial Random Variable
 E.  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 Table III in Appendix A
    c. Individual probabilities and cumulative probabilities
  3. Mean, Variance, and Standard Deviation of a Poisson Random Variable

V. Continuous Probability Distributions
 A.  Probability Density Functions
   1. Properties of a Density Function
   2. Probabilities for Continuous Random Variables
     a.  Probability a r.v. falls within a certain INTERVAL
     b.  Area under the density curve
 B.  Uniform Distribution
   1. Density Function for a Uniform r.v.
   2. Mean of a Uniform r.v.
   3. Std. deviation of a Uniform r.v.
   4. Probability a Uniform r.v. falls in a certain interval
 C.  Normal Distribution
   1. Role of mu and sigma in the normal distribution
   2. The Standard Normal and its Characteristics
   3. Finding Probabilities Involving Standard Normal Random Variables
     a.  Using Table IV to find areas under standard normal curve
     b.  Finding z-values that correspond to specified areas/probabilities
   4. Standardizing Normal Random Variables
     a. Finding Probabilities Involving any Normal Random Variable
     b. "Unstandardizing" z-values 
 D.  Normal Approximation to the Binomial
   1.  Why can we use this approximation?
   2.  When is it appropriate?  (Rule of Thumb)
   3.  Using the continuity correction