STAT 515 -- EXAM 2 REVIEW SHEET 

I.  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

II. 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)

III. 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. Estimation of a Parameter
     a.  Point Estimation
     b.  Unbiased statistic
     c.  Standard Error of a Statistic  
   2. Pattern of Variability of the Sample Mean Across Repeated Samples
   3. Mean of Sampling Distn. of X-bar
   4. Std. Deviation (Std. Error) of Sampling Distn. of X-bar
   5. 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?
 C.  Using the Sampling Distribution of the Sample Mean
   1.  Using Normal Distribution Techniques to Find Probabilities involving X-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

IV.  Confidence Intervals
 A. Precise Interpretation of a Confidence Interval
   1.  What does, for example, "95 percent confidence" mean exactly?
 B. Relationship among confidence level, sample size, and width of the CI
 C. Small-sample Confidence Intervals about a Mean (when sigma unknown)
   1. Sampling distribution of "t-statistic" (t distribution)
   2. How is t distribution different from standard normal?
   3. Reading Table VI to get critical t values
   4. Formula for CI for mu
 D. Confidence Intervals about a Proportion
   1. Definition of Sample proportion (p-hat)
   2. Sampling Distribution of p-hat
   3. Classical CI for p
   4. When can we use this formula? (rules of thumb)
   5. Agresti-Coull CI for p
 E. Other Confince Intervals
   1. Confidence interval for the variance sigma^2 (and for sigma)
   2. Confidence interval for the ratio of two variances
 F. Sample Size Determination
   1. Sample size determination for CI about mu
   5. Sample size determination for CI about p