STAT 509 -- EXAM 1 REVIEW SHEET 

I.  Introduction to Probability
  A. Key Terms
   1. Experiment
   2. Outcome
   3. Sample Space (and Sample Points)
   4. Event
  B. Compound Events
   1. Unions and Intersections
   2. Understanding the meaning of each compound event
   3. Venn Diagrams
   4. Mutually exclusive events
   5. Additive Rule (Probability of Union of Two Events)
  C. Complement of an Event
  D. Conditional Probability
   1. Definition of Conditional Probability
   2. Multiplicative Rule (Probability of Intersection of Two Events)
   3. Independent Events
      a. Intuitive definition of independent events
      b. Mathematical definition of independent events 
      c. Random samples and independence
  E. Bayes' Rule

II.  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
  4.  Determining Validity of a Probability Distribution
 C.  Cumulative Distribution Function
  1.  Definition of a cdf
  2.  Deriving the cdf for a discrete distribution
  3.  Graph of the cdf for a discrete distribution
 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
  4.  Rules for Expected values and Variances 
 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 R for cumulative binomial probabilities
  4. Mean, Variance, and Standard Deviation of a Binomial Random Variable
 E.  Hypergeometric Random Variables
  1.  Difference between Hypergeometric and Binomial sampling situations
  2.  Using the Hypergeometric probability formula
  3.  Hypergeometric mean
 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 R for cumulative Poisson probabilities
  3. Mean, Variance, and Standard Deviation of a Poisson Random Variable
  4. Poisson Probabities for Counts across t units of time/space
  5. Conditions for a Poisson Process

III. 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
     c.  Finding probabilities by integrating density functions
   3. Cumulative Distribution Function
     a.  Definition of a cdf
     b.  Deriving the cdf for a continuous distribution
 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.  Exponential Distribution
   1. Using the exponential density function
   2. Mean and variance of an exponential distribution
   3. Simple formula for exponential probabilities
   4. Relationship between exponential and Poisson distributions
 D.  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 1 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 

IV. Sample Variability and Sampling Distributions
 A.  Statistics and Parameters
   1.  Examples of each
   2.  What is the difference between a statistic and a parameter?
 B. Definition of a Sampling Distribution
   1. Pattern of Variability of the Sample Mean Across Repeated Samples
   2. Mean of Sampling Distn. of Y-bar
   3. Std. Deviation (Std. Error) of Sampling Distn. of Y-bar
   4. Shape of Sampling Distn. of Y-bar
     a.  When original data are normally distributed?  When data are not normal?
     b.  Central Limit Theorem (CLT)
     c.  When does the CLT apply?
   5. Q-Q plots and checking normality
 C.  Using the Sampling Distribution of the Sample Mean
   1.  Using Normal Distribution Techniques to Find Probabilities involving Y-bar
 D. Other Sampling Distributions
   1. t-distribution
   2. Chi-square distribution
   3. F-distribution
   4. What are the shapes of these distributions?
   5. What do "degrees of freedom" signify for these distributions?
   6. Reading t, chi-square, and F tables in textbook