All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Share

Description

2

Tags

Transcript

Discrete Random Variables
Distribution, Expectation, Variance
Random Variable
ã
A random variable is a function whose domain is the sample space and
whose range is a subset of the set of real numbers.
ã
A random variable is a function that associates a unique numerical value with every outcome of an experiment. The value of the random variable will vary from trial to trial as the experiment is repeated. * Experiment : Toss a coin twice Sample Space : {HH, HT, TH, TT} X = number of heads X(HH) = 2, X(HT) = 1, X(TH) = 1, X(TT) = 0 X :
Ω
{0,1,2} is a function. Hence X is a random variable (*http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#randvar )
Experiment : Draw three balls at random from an urn containing two red and two green balls.
Sample Space = {RRG, RGG} X = number of red balls X(RRG) = 2, X(RGG) = 1 X :
Ω
{1,2} is a function. Hence X is a random variable. Experiment : Toss two dice.
Sample Space = {(1,1), (1,2),…, (1,6),…, (6,1),…(6,6)}
X = sum of the scores obtained in the two tosses
X((1,1)) = 2, X((1,2)) = 3, …, X((6,6)) = 12
X :
Ω
{2, …,12} is a function.
X is a random variable
Discrete Random Variable
ã
A random variable is said to be discrete if the range of values taken by the random variable is either finite or is countably infinite.
ã
All the examples of random variables given till now are discrete random variables
ã
An example of a random variable which is not discrete is given below : Experiment : Choose three students at random from PGP-1 Sample Space : {{a, b, c}: a, b, c are students of PGP-1} X = total sum of weights of the three students in fitness center X can take any positive value. Hence X is not a discrete random variable.

Related Search

Previous Document

Next Document

Related Documents

Sep 20, 2017

Sep 20, 2017

Sep 20, 2017

Sep 21, 2017

Sep 21, 2017

Sep 21, 2017

Sep 21, 2017

Sep 22, 2017

Sep 24, 2017

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks