Tests for MATH/STAT 511
Probability
Tests and Other Resources
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 Test 1
Solutions
[Sections of Text covered: 2.12.5; 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 3.13.4, use of Excel for computation and
synthetic experiments]
Objectives:
 Know the definitions of
 the Bernoulli, Binomial, and the Hypergeometric
distributions and the types of random variables with
which they are most often associated,
 expectation of a random variable and others related to it, including
its moments E[X], E[X^{2}], ... 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. 45 and
Chapter 4, Sect. 14 from the Text]
Objectives:
 Know the definitions of the following probability distributions and the uses
of the random variable models that they typically represent:
 Discrete: Poisson, geometric, and negative binomial
 Continuous: uniform, exponential, gamma, chi^{2}, 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 13 will be approximately 80% of
the Final Exam, the remaining 20% will cover jointly distributed random
variables. These last sections covered are Sections 5.15.3; 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:




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