Math 310 & Stat 410 at Lehigh University
Math 310/Stat 410 (Probability and Its Applications): Random
moment-generating and characteristic functions; limit theorems;
processes, Kolmogorov euqations; Markov chains, random walks.
Math 309 or consent of the department chairperson. (Poisson processes
applications on queuing theory and reliability theory are included in
the course. Brownian motion and stationary processes and applications
pricing stock options are typically included in the course.)
Here is a typical course description.
This course can be taken as a 400-level (3 graduate credits).
The text is `Introduction to probability Models', 6th edition, by S.
Topics to be covered:
Review (sample space, probability measure, conditional probability,
randon variables, some known discrete and continuous distributions,
distributions, expected values, variance, covariance).
Moments and Moment generating function.
Can moments always uniquely determine a probability distributions?
The moment-generating technique
Limit theorems (Convergence in probability, LLN, Central Limit Theorem,
and convergence in distribution).
Markov's Inequality; Chebyshev's Inequality; Boole's Inequality;
Conditional probability and conditional expectation
Computing probabilities by conditioning
Computing expectations by conditioning
Recursive equations and the method of conditioning
Classification of states
Birth and death chains
Limiting and stationary probabilities of markov chains
Exponential and Poisson distributions
Interarrival and waiting time distributions
Nonhomogeneous and compound processes
Birth and death process
The Kolmogorov differential equations
Some applications in queueing theory
Random walks and Brownian motion
Other special topics
Please contact Professor Wei-Min Huang, Department of Mathematics,
for further information. To contact me, send e-mail to wh02@Lehigh.EDU,
or click here
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supports forms. Click for Lehigh's home page or for
Mathematics Department home page.
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