<< Chapter < Page Chapter >> Page >
This module contains a set of definitions from statistics that might be useful for advanced undergraduates.

Important definitions in statistics

It is not unusual for students to forget important concepts learned in an earlier course. This set of definitions is intended to stir memories of those wonderful times when you were learning statistics and econometrics. It is not intended to replace a statistics course but to provide you with a handy guide to the denfinition of some important terms in the statistical tools used by economists.

Random variables

Random experiment

A random experiment is an experiment whose outcome is uncertain.

Outcome space

The outcome space (also sometimes referred to as the sample space) is the list of all possible outcomes of a random experiment.

Single toss of a coin.

Consider the toss of a coin. Since the outcome is uncertain, tossing the coin is an example of a random experiment. The outcome space consists of a heads and a tails. If we let X be 0 if the outcome is a heads and let X equal 1 if the outcome is a tails, then X is a random variable. Since X only can take on integer values (0 or 1), it is a discrete random variable.

Random variable

A random variable is a number that can be assigned to an outcome of a random experiment. A discrete random variable has a finite number of possible values while a continuous random variable has an infinite number of potential values.

Non-stochastic variable

A non-stochastic variable is any variable that is not a random variable; i.e., does not represent the outcome of a random experiment.

Multiple tosses of a coin.

Let x equal the number of heads that occur when a coin is tossed n times. The tossing of the coin n times is a random experiment. The outcome space of this random experiment is an integar between 0 and n . Since the value x is equal represents the outcome of a random experiment, it is a random variable.

Random sample

A random sample of size n out of a population of size N has the characteristic that every member of the population is equally likely to be chosen.

Height of college age women.

Consider a random sample of the population of college age women. The height, x , of any woman chosen from this population is a random variable with a value somewhere in the outcome space, where the outcome space is a number between (say) 24 and 96 inches. Since in theory we can have as accurate a measurement as we might like, x can be thought of as being a continuous random variable.

Probability

General terms

Probability distribution for a discrete random variable.

Consider a discrete random variable x i MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadIhadaWgaaWcbaGaamyAaaqabaaaaa@3800@ that represents an outcome of the n potential outcomes of a random experiment—that is, the set of potential outcomes is represented by X = ( x 1 , , x n ) . MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaahIfacqGH9aqpdaqadaqaaiaadIhadaWgaaWcbaGaaGymaaqabaGccaGGSaGaeSOjGSKaaiilaiaadIhadaWgaaWcbaGaamOBaaqabaaakiaawIcacaGLPaaacaGGUaaaaa@40A1@ Pr ( x i ) MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGaccfacaGGYbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaaGccaGLOaGaayzkaaaaaa@3B5F@ Any function is a probability if and only if (1) Pr ( x i ) 0  for all  i = 1 , , n , MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGaccfacaGGYbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaaGccaGLOaGaayzkaaGaeyyzImRaaGimaiaabccacaqGMbGaae4BaiaabkhacaqGGaGaaeyyaiaabYgacaqGSbGaaeiiaiaadMgacqGH9aqpcaaIXaGaaiilaiablAciljaacYcacaWGUbGaaiilaaaa@4C2E@ (2) Pr ( x i x j ) = Pr ( x i ) + Pr ( x j ) MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGaccfacaGGYbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaOGaeyOkIGSaamiEamaaBaaaleaacaWGQbaabeaaaOGaayjkaiaawMcaaiabg2da9iGaccfacaGGYbWaaeWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaaGccaGLOaGaayzkaaGaey4kaSIaciiuaiaackhadaqadaqaaiaadIhadaWgaaWcbaGaamOAaaqabaaakiaawIcacaGLPaaaaaa@4BF6@ for all i and j, and (3) i = 1 n Pr ( x i ) = 1. MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaaqahabaGaciiuaiaackhadaqadaqaaiaadIhadaWgaaWcbaGaamyAaaqabaaakiaawIcacaGLPaaaaSqaaiaadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aOGaeyypa0JaaGymaiaac6caaaa@43C0@ An example of a discrete distribution is in Example 4.

Discrete distribution.

Figure 1 illustrates a discrete probability distribution where x i MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadIhadaWgaaWcbaGaamyAaaqabaaaaa@3800@ goes from 1 to 8. The areas in the shaded rectangles sum to 1.

A discrete probability function

Graph of a discrete probability function.
The areas of the rectangles sum to 1.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Econometrics for honors students. OpenStax CNX. Jul 20, 2010 Download for free at http://cnx.org/content/col11208/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Econometrics for honors students' conversation and receive update notifications?

Ask