Tests for MATH/STAT 511
Probability

## Tests and Other Resources

To view an Acrobat PDF version of each test, click on the symbol .   Free reader here.
To view a compressed postscript file, click on the symbol .  Free reader here.

• 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 MX(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[Xr] 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
```

• Math 511 Tests- Spring 2000, Professor Howard
(These are given in Adobe PDF Format.)
• Math 511 Tests, Professor Sumner.

The Probability site developed by Professor Sumner has an excellent set of problems, sample test problems, programs and probabilistic simulations. (Some the sample tests and answers are given in Adobe PDF Format.)
•  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