STAT333 Lecture Notes - Lecture 9: Equivalence Class, Identity Matrix, Random Variable

• School: University of Waterloo
• Department: Statistics
• Course: STAT333
• Professor: Steve Drekic

Document Summary

Generally speaking, {x(t), t t} is called a stochastic process if x(t) is a random variable (or random vector) for any xed t t . T is referred to as the index set , and is often interpreted in the context of time. As such, x(t) is often called the state of the process at time t . The index set t can be a continuum of values (e. g. , t = {t : t 0}) or can be a set of discrete points such as t = {t0, t1, t2, . Since there is a one-to-one correspondence with the set of non-negative integers {0, 1, 2, . }, we will use such an index set for a discrete-time process. In other words, {x(n), n = 0, 1, 2, . (or {xn, n = 0, 1, 2, . will represent a general discrete-time stochastic process.