STAT 512 -- EXAM 2 REVIEW SHEET 

I.  Basic Ideas in Inference
  A. Definition of Random Sample
  B. Definition of Statistic
  C. Sampling Distribution of a Statistic
II. Sampling Distributions when we have Normal Data
  A.  Sampling Distribution of the Sample Mean Y-bar
     1. Expected Value of Y-bar
     2. Variance of Y-bar
     3. Proof of Normality of Y-bar (when data are normal)
     4. Finding probabilities about Y-bar
  B.  The Chi-square Distribution
     1. Relationship to gamma distribution
     2. Sum of independent chi-square r.v.'s
     3. Other theorem relating two chi-square r.v.'s
  C.  Sampling Distribution of the Sample Variance S^2
     1. When are Y-bar and S^2 independent r.v.'s?
     2. Distribution of (n-1)S^2/(sigma^2) when data are normal
     3. Finding probabilities about S^2
  D.  The t Distribution
     1. Definition of a t r.v. (in terms of normal and chi-square r.v.'s)
     2. "Degrees of freedom' for a t r.v.
     3. Expected value of the reciprocal of a chi-square r.v.
     4. Expected value and variance of a t r.v.
     5. Relationship/comparison of the t and Z (std. normal) distributions 
  E.  Relationship between Y-bar and the t-distribution
     1. Sampling Distribution of the (Y-bar - mu)/[S/sqrt(n)]
     2. Distribution of (n-1)S^2/(sigma^2) when data are normal
     3. Finding probabilities about Y-bar when sigma^2 is unknown
  F.  The F Distribution
     1. Definition of a F r.v. (in terms of two indep. chi-square r.v.'s)
     2. Numerator and Denominator "Degrees of freedom' for an F r.v.
     3. Expected value and variance of an F r.v.
     4. Other properties of F r.v.'s
     5. Finding probabilities about the ratio of two sample variances
III. The Central Limit Theorem
  A.  Precise Formal Statement of the Central Limit Theorem
  B.  Implications of the Central Limit Theorem
     1. Behavior of Y-bar when the sample size is large
     2. Finding probabilities about Y-bar when the sample size is large
     3. Rules of Thumb about how large n should be to apply the CLT
IV. The Normal Approximation to the Binomial
  A.  Facts about Binomial Experiments
     1. Definition of p-hat in a binomial experiment
     2. Approximate Distribution of p-hat when n is "large"
     3. Approximate Distribution of # of successes Y when n is large

***** The following will not be on Test 2 in Spring 2014: *****
  B.  Using Normal Probability to approximate a Binomial probability
     1. Correct mean and variance of the normal distribution
     2. Correct use of the Continuity Correction
     3. Rule of thumb for when the Normal approximation works well
  C.  Normal approximation to other Discrete Distributions (e.g., Poisson)