Tests for MATH/STAT 511
Probability

Tests and Other Resources

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• Test 1       Solutions  
  
  [Sections of Text covered:   2.1-2.5; 3.1, 3.3 (Binomial dist. only)]
  
  Objectives:
  • Know the definitions of permutations, combinations, distinguishable permuations, the hypergeometric distribution, Bernoulli trials, and the Binomial distribution.
  • Know the "formal definitions" of Probability, conditional probability, mutually independent events, random variable, and the probability mass function of a random variable.
  • Know the statement of the Multiplication Principle, the Multiplication Rule for probabilities, and Bayes' Theorem.
  • Know how to prove properties of probability (e.g. P(A B) = P(A) +P(B) - P(AB), ...), Bayes' Theorem, properties of independence.
  • Finally, be able to compute using enumeration techniques and apply them to probabilities and random variables, as, for example done in the assigned homework.
  
  
• Test 2       Solutions  
  
  [Material covered:   Text Sections 3.1-3.4, use of Excel for computation and synthetic experiments]
  
  Objectives:
  • Know the definitions of
    1. the Bernoulli, Binomial, and the Hypergeometric distributions and the types of random variables with which they are most often associated,
    2. expectation of a random variable and others related to it, including its moments E[X], E[X²], ... and the moment generating function M_X(t) of a random variable X.
  • Know the statements and proofs of the properties of mathematical expectation including the formulas for E[X] for specific distributions.
  • Know the properties of the moment generating function, and how to compute and apply them. Understand how the MGF "encodes" the moments E[X^r] and the probability mass function for a random variable. Be able to derive the MGF for the Binomial Distribution.
  
  
• Test 3       Solutions  
  
  [Material covered:   Chapter 3, Sect. 4-5 and Chapter 4, Sect. 1-4 from the Text]
  
  Objectives:
  • Know the definitions of the following probability distributions and the uses of the random variable models that they typically represent:
    1. Discrete:   Poisson, geometric, and negative binomial
    2. Continuous:   uniform, exponential, gamma, chi², and standard normal
    Emphasis is placed on those that are bolded.
  • Be able to compute the moments and moment generating functions for these random variables (both continuous and discrete).
  • Be able to apply these random variables, i.e. `word problems'.
  
  
• Final Exam    
  
  [Material covered:   Material from Test 1-3 will be approximately 80% of the Final Exam, the remaining 20% will cover jointly distributed random variables. These last sections covered are Sections 5.1-5.3; 61.-6.2. Although Section 6.8 was covered in class, it was announced that it will not be on tbe Final Exam.
  
  Objectives:
  • Be able to compute probabilities for joint probability distributions.
  • Be able to compute marginal and conditional distributions, correlation coefficients, and expectations for random variables with joint distributions.
  • Know the properties of independent random variables.
  • Be able to work with sums of independent random variables and their moment generating functions.


Course Grades turned in Thursday, May 10 at 2 pm.


    Code       Test 1 Test 2  Test 3  HW  Exam Course Letter
     -----      ------ ------ ------ ---  ---- ------ ------
     2541         52     70    52    87    67    57      C
     2099         86    100   100   103   150    97      A+
     HMKK         56     61    59    48    99    60      C
     SHORT        86     87    89    68   114    82      B+
     HOUSE        62     93    65    92    89    71      B
     2789         59     77    53    90    73    61      C
     9023         98     98    95   103   146    98      A+
     4855         45     73    50    75    92    60      C
     3334         34     55    44    51    76    47      D
     1198         84     87    67    73    97    74      B
     4728         83     93    80    92   143    89      A
     JDJNW        36     58    31    47    71    44      D

Links to additional sample tests and resources:

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated December 3, 2000.  This page ©1997-2000, The Board of Trustees of the University of South Carolina.  URL: http://www.,math.sc.edu/~sharpley/math511