Chapter 3 (3.1 - 3.3) 2114

Chapter 3 (3.1 - 3.3) 2114 - Discreterandomvariablesand

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Discrete random variables and  probability distributions Chapter 3 (3.1 – 3.3) 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 For a given sample space S of some experiment, a random variable is any rule that associates a number with each outcome in S . Random Variables Examples: die toss, number of defects in a sample of 100 products, number of experimental trials before success, number of people who will vote for a particular candidate, weight of a coil of steel, length of a steel beam, diameter of a washer, etc.
Background image of page 2
3 Random Variables Any random variable whose only possible values are 0 and 1 is called a Bernoulli random variable . Variable means different numerical values are possible and random means the observed value depends on which of the possible experimental outcomes results
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Types of Random Variables A discrete random variable is an rv whose possible values either constitute a finite set or else can listed in an infinite sequence. A random variable is continuous if its set of possible values consists of an entire interval on a number line (and is always infinite).
Background image of page 4
Notation 5 rv - random variable Upper case (capital) letters - X, Y, Z - denote different random variables X(s) = x; means that x is the number associated with the outcome s by the rv X , so x is called the value of the variable associated with s .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Examples: 6 Are the following random variables discrete or continuous? finite or infinite? The total number of points scored in a football game. The shelf life of a particular drug. The height of the ocean's tide at a given location. The length of a two-year old black bass. The number of aircraft near-collisions last year.
Background image of page 6
7 Probability Distribution The probability distribution or probability mass function (pmf) of a discrete rv is defined for every number x by p ( x ) = S (all : ( ) ). P s X s x =
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 The Probability Distribution for a random variable X tells us how the total probability of 1 for the sample space S is distributed among each of the mutually exclusive simple events (or
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/17/2011 for the course ENGR 0020 taught by Professor Rajgopal during the Spring '08 term at Pittsburgh.

Page1 / 27

Chapter 3 (3.1 - 3.3) 2114 - Discreterandomvariablesand

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online