MAT 4371 : MAT4371 Summary.docx

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 4371
• Professor: Francois Theberge

Document Summary

Sample space: the set of all possible outcomes of an experiment, denoted as the set . (example: the sample space of flipping a coin is . ) Alternate definition: the sample space is a set which has a 1-to-1 correspondence with the outcomes of a random experiment. Discrete-time stochastic process: suppose the random experiment with sample space if performed once per time unit. We define the sample space of the composite experiment consisting of the sequence of simple experiments as , called a discrete-time stochastic process. Algebra: a collection f of subsets is a -algebra if: (closed under complementation) (countable union). Total information: if , we say we have total information. If not, we say we have partial information. Event: any subset of the sample space . (example: the event that the coin lands on heads; then. We say that the event occurs when the outcome of the experiment lies in .