STAT 410 (Introduction to Probability Theory)
| DESCRIPTION |
The course is a solid introduction to the
formulation and manipulation of probability models, leading up to a
rigorous proof of the law of large numbers and the central limit
theorem. The emphasis is on concepts: sets and combinatorics allow a
precise mathematical formulation of probability models, multivariable
calculus supplies machinery for changing variables and calculating
probabilities and average values relating to vectors of real-valued
random variables, and limit theorems allow event-occurrences which are
individually unpredictable to become predictable in the aggregate. |
| PREREQUISITES |
Math 240 and Math 241. |
| TOPICS |
Text of Ross, chapters 1-8 including:
Axioms of Probability and basic
properties
Combinatorial problems
Conditional probability
Random
variables and distributions in one and several variables, including
change-of-variable techniques
Expectation and conditional
expectation
Moments
Moment generating functions
Law of Large
Numbers and Central Limit Theorem
Optional Topics from among:
Characteristic functions
Fourier transforms
Borel-Cantelli Lemma
Meaning of convergence
with probability 1
Filling in missing steps of the book's proof
of the Central Limit Theorem
|
| TEXT |
Text(s)
typically used in this course. |
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