STAT 511 -- EXAM 2 REVIEW SHEET 

I. More Special Discrete Probability Distributions

 A.  The Hypergeometric Distribution
  1.  Sampling structure for a hypergeometric-type experiment
  2.  Difference between binomial experiment and hypergeometric-type experiment
  3.  Hypergeometric probability function
     a. Finding hypergeometric probabilities using the probability formula
  4.  Mean of a hypergeometric r.v.
  5.  Variance and standard deviation of a hypergeometric r.v.
  6.  Relationship between binomial and hypergeometric r.v.'s
     a. Using binomial probabilities to approximate hypergeometric probabilities
     b. When is this approximation valid?
 B.  The Poisson Distribution
  1.  Motivation for Poisson as a limit of binomial probabilities 
  2.  Poisson probability function
  3.  Finding Poisson probabilities using the probability formula
  4.  Finding (cumulative) Poisson probabilities using Table 3
  5.  Mean of a Poisson r.v.
  6.  Variance and standard deviation of a Poisson r.v.
  7.  Relationship between binomial and Poisson r.v.'s
     a. Using Poisson probabilities to approximate binomial probabilities
     b. When is this approximation valid?

II.  More about Probability Distributions
 A.  Moments and Moment-generating Functions
  1.  Basic Definition of the k-th Moment
     a.  Some special moments of interest
     b.  Moments about the mean
  2.  Definition of the mgf
     a.  When does the mgf exist?
  3.  Relationship between the mgf and the moments of a r.v.
     a.  How do we use the mgf to get the k-th moment?
     b.  Why does this work?
  4.  Examples of finding mean and variance of various r.v.'s using mgf's
  5. The mgf uniquely characterizing a distribution
     a.  Using the form of a mgf to identify the specific distribution of a r.v.
 B.  Continuous Random Variables
  1.  Support of a r.v.
     a.  What characterizes the support of a continuous r.v.?
 C.  Continuous Probability Distributions
  1.  Definition of the cdf of a r.v.
     a. Finding the cdf of a discrete r.v.
     b. Properties of any cdf
     c. Difference between the cdf of a discrete r.v. and cdf of a continuous r.v.
     d. Finding probabilities using the cdf
  2.  Probability density function (pdf)
     a. Relationship between cdf and pdf of a continuous r.v.
     b. Properties of any pdf
     c. Finding a pdf, if given a cdf
     d. Finding a cdf, if given a pdf
     e. Graphing a cdf and/or a pdf
     f. Finding probabilities using the pdf
     g. Solving for a constant that yields a valid pdf
  3.  Quantiles of a r.v.
     a. Definition of a quantile
     b. Finding a quantile for a continuous r.v.
     c. Median of a continuous r.v.
 D.  Expected Value of a continuous r.v.
   1. Definition of expected value of a continuous r.v.
   2. Expected Value of a function of a r.v.
   3. Definition of variance
   4. Finding expected value and variance for a given continuous probability distribution 

III. Special Continuous Distributions
 A.  Uniform Distribution
  1.  Using the Uniform pdf to obtain probabilities
  2.  The nature of the Uniform cdf
  3.  Using the Uniform mean and variance
  4.  Relationship between a Poisson Process and the Uniform Distribution
 B.  Moment-generating Functions for Continuous r.v.'s
  1.  Definition of moments of a continuous r.v.
  2.  Definition of moment-generating function of a continuous r.v.
  3.  Process for deriving specific moments using the mgf