##
Math 310 & Stat 410 at Lehigh University

**Math 310/Stat 410 (Probability and Its Applications): Random
variables,
moment-generating and characteristic functions; limit theorems;
stochastic
processes, Kolmogorov euqations; Markov chains, random walks.
Prerequisite:
Math 309 or consent of the department chairperson. (Poisson processes
and
applications on queuing theory and reliability theory are included in
the course. Brownian motion and stationary processes and applications
to
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.
Ross.

Topics to be covered:

Review (sample space, probability measure, conditional probability,
independence,
randon variables, some known discrete and continuous distributions,
joint
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
Markov chains
Transition probabilities
Hitting times
Chapman-Kolmogorov equations
Classification of states
Induced martingales
Birth and death chains
Limiting and stationary probabilities of markov chains
Exponential and Poisson distributions
Poisson process
Counting process
Interarrival and waiting time distributions
Nonhomogeneous and compound processes
Birth and death process
The Kolmogorov differential equations
Time reversibility
Uniformization
Renewal process
Some applications in queueing theory
Random walks and Brownian motion
White noise
Simulation
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
Mail-Me, if your web server
supports forms. Click for Lehigh's home page or for
Lehigh
Mathematics Department home page.
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