random variables & probability distributions
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Random Variables & Probability DistributionsTRANSCRIPT
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Quality Engineering & Management
Session 2.2: Random Variables & Probability Distributions
Dr. Holly Ott Production and Supply Chain Management
Chair: Prof. Martin Grunow TUM School of Management
Holly Ott Quality Engineering & Management Module 2.2 1
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Learning Objectives
List the properties and types of random variables. Understand the meaning of probability distribution functions for
discrete and continuous variables.
Describe the cumulative distribution function. Define the mean and variance for a probability distribution
functions.
Review several important distribution functions.
Holly Ott Quality Engineering & Management Module 2.2 2
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Random Variables
A random variable is a variable, which assumes for its values the outcomes of a random experiment.
A random variable assumes only real numbers.
The set of all possible values of a random variable X is called its range space.
Events can be defined in the range space and their probabilities can be found.
2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
Holly Ott Quality Engineering & Management Module 2.2 3
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Random Variables
Holly Ott Quality Engineering & Management Module 2.2 4
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Random variables are of two kinds: 1. Discrete random variables 2. Continuous random variables.
A discrete random variable takes a finite (or countably infinite)
number of possible values.
A continuous random variable takes an infinite number of possible values; it takes values in an interval.
Random Variables
2012 from "A First Course in Quality Engineering: Integrating Statistical and Management Methods of Quality" by K.S. Krishnamoorthi. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
Holly Ott Quality Engineering & Management Module 2.2 5
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Random Variables
Holly Ott Quality Engineering & Management Module 2.2 6
Foto: Lupo / pixelio.de
Foto: Lupo /pixelio.de
Foto: Antje Delater / pixelio.de
Foto: neurolle - Rolf / pixelio.de
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Random Variables
Foto: Rosemarie Doll / www.pixelio.de
Holly Ott Quality Engineering & Management Module 2.2 7
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Ergebnisse sind normal-verteilt, wenn sie von vielen Einssen abhngen
Height
Frequency
Reiner Hutwelker
X = the height of people entering a test at the Munich Oktoberfest.
Random Variables
Holly Ott Quality Engineering & Management Module 2.2 8
Foto: Michaela Schllhorn / pixelio.de
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Ergebnisse sind normal-verteilt, wenn sie von vielen Einssen abhngen
Height
Frequency
Reiner Hutwelker
X = the height of people entering a test at the Munich Oktoberfest.
Random Variables
Holly Ott Quality Engineering & Management Module 2.2 9
Foto: Michaela Schllhorn / pixelio.de
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TUM School of Management Production and Supply Chain Management Prof Martin Grunow Technische Universitt Mnchen
Exercise
Now look at the next video to see an example of a random variable.
Holly Ott Quality Engineering & Management Module 2.2 10
Foto: Wolfgang Dirscherl / www.pixelio.de