SCCC 312A -- EXAM 2 REVIEW SHEET

I.  Introduction to Probability
  A. Notion of Randomness
   1. Empirical probability (Relative Frequency)
   2. Theoretical Probability
   3. Law of Large Numbers
  B. Key Terms
   1. Experiment
   2. Outcome
   3. Sample Space (and Sample Points)
   4. Event
  C. Three Viewpoints on Probability
   1. "Equally Likely" Concept of Probability
   2. "Long-Run Relative Frequency" Concept of Probability
   3. Subjective Probability
  D. Three Major Probability Rules
  E. Complement of an Event
  F. Compound Event
   1. What are the three main compound events we discussed?
   2. Understanding the meaning of each compound event
   3. Mutually exclusive events
   4. Special Addition Rule for m.e. events
   5. General Addition Rule
   6. Independent Events
      a. Intuitive definition of independent events
      b. Mathematical definition of independent events
   7. Conditional Probability
   8. Special Multiplication Rule for Independent Events
   9. General Multiplication Rule
   10. Distinction between independent events and m.e. events

II.  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.  Statistics and Parameters
  1.  Examples of each
  2.  What is the difference between a statistic and a parameter?
 D.  Determining the Population Mean and Variance of a Discrete r.v.
  1.  Formula for Popn. Mean mu
  2.  Formula for Popn. Variance sigma^2
  3.  Popn. Standard Deviation sigma
 E.  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 2 in Appendix B
    c. Individual probabilities and cumulative probabilities
  4. Mean, Variance, and Standard Deviation of a Binomial Random Variable

III. Normal Probability Distributions
 A.  Continuous Distributions and Density Curves
   1. Properties of a Density Curve
   2. Probabilities for Continuous Random Variables
     a.  Probability a r.v. falls within a certain INTERVAL
     b.  Area under the density curve 
 B.  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 3 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 
 C.  Normal Approximation to the Binomial
   1.  Why can we use this approximation?
   2.  When is it appropriate?  (Rule of Thumb)
   3.  "Continuity Correction"

IV. Sample Variability and Sampling Distributions
 A. Definition of a Sampling Distribution
   1. Pattern of Variability of the Sample Mean Across Repeated Samples
   2. Mean of Sampling Distn. of X-bar
   3. Std. Deviation (Std. Error) of Sampling Distn. of X-bar
   4. Shape of Sampling Distn. of X-bar
     a.  When original data are normally distributed?  When data are not normal?
     b.  Central Limit Theorem (CLT)
     c.  When does the CLT apply?
 B.  Using the Sampling Distribution of the Sample Mean
   1.  Using Normal Distribution Techniques to Find Probabilities involving X-bar