Chapter 3 (3.1 - 3.3) 2114

# Chapter 3 (3.1 - 3.3) 2114 - Discreterandomvariablesand

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Discrete random variables and  probability distributions Chapter 3 (3.1 – 3.3) 1

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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.
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

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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).
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 .

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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.
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 =

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

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Chapter 3 (3.1 - 3.3) 2114 - Discreterandomvariablesand

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