##### Personal tools
•
You are here: Home Introduction; Review of Random Variables

# Introduction; Review of Random Variables

##### Document Actions

Probability   ::   Set Theory   ::   Definition   ::   Conditional   ::   Random   ::   Distribution   ::   R.V.S.

## Set theory

Probability is intrinsically tied to set theory. We will review some set theory concepts.

We will use to denote complementation of a set with respect to its universe.

- union: is the set of elements that are in or .

- intersection: is the set of elements that are in and . We will also denote this as .

: is an element of the set .

: is a subset of .

: and .

Note that

(where is the universe).

Notation for some special sets:

- set of all real numbers

- set of all integers

- set of all positive integers

- set of all natural numbers, 0,1,2,...,

- set of all tuples of real numbers

- set of complex numbers

That is, if is a field and , then must also be in (closed under complementation). If and are in (which we will write as ) then .

Note: the properties of a field imply that is also closed under finite intersection. (DeMorgan's law: )

What do we mean by countable?

• A set with a finite number in it is countable.
• A set whose elements can be matched one-for-one with is countable (even if it has an infinite number of elements!)
Are there non-countable sets?

Note: For any collection of sets, there is a -field containing , denoted by . This is called the -field generated by .

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 31). Introduction; Review of Random Variables. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lec1_2.html. This work is licensed under a Creative Commons License