Principles of Applied Probability

Synopsis

Chance plays an important part in all aspect of life. We take chances everyday: whether we catch the bus or just miss it; whether or not we are caught in a sudden shower. Chance or random variations is also an essential features of almost all working systems: scientist taking measurements in a laboratory; an economist studying price fluctuations; a surgeon studying heartbeat patterns on a electrocardiogram. In all theses processes, some elements of chance or randomness are present.MTH306 deals with some of these random phenomena, the emphasis being on modeling and problem solving. A practical situation is described and then a probability model is developed to describe the main features. The model is then analyzed mathematically in order to discover the possible ways in which the situation might develop, and the probabilities associated with them.

Level: 3
Credit Units: 5
Presentation Pattern: Every July

Topics

Probabilities.
Random variables.
Random processes.
Point and types of point process.
Branching processes.
The Poisson distribution.
Random walks.
Stochastic processes.
Markov chain.
Applications of Markov chain.
Birth processes.
Death processes.

Learning Outcome

Calculate the expectation/variance/cumulative distribution functions or probability generating functions of random variables.
Show how to prove a mathematical statement in stochastic processes.
Determine the reducibility and/or periodicity of a given Markov chain.
Solve for the general solution of the partial differential equation of some probability generating function.
Compute probabilities of events.
Discuss the results obtained or whether a Stochastic model is suitable.

Part-time Programmes / CET Courses

Singapore University of Social Sciences

Principles of Applied Probability