# Lecture18 - DSAP NUS Semester 1 2008/2009 – 146 L ONG-R...

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DSAP, NUS, Semester 1, 2008/2009 – 1 GEM2900: Understanding Berwin Turlach Department of Statistics and Applied Probability National University of Singapore

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Expected value or mean DSAP, NUS, Semester 1, 2008/2009 – 145 Let X be a discrete random variable with set of possible values D and p.m.f. p X ( x ) . The expected value or mean value of X , denoted by E[ X ] or μ X , is E[ X ] = μ X = s x D x · p X ( x ) Let X be a continuous random variable X with p.d.f. f X ( x ) The expected value or mean value of X , denoted by E[ X ] or μ X , is E[ X ] = μ X = i -∞ u · f X ( u ) du
Interpretations of the expected value
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Unformatted text preview: DSAP, NUS, Semester 1, 2008/2009 – 146 L ONG-R UN A VERAGE : if we observe the random variable X many times, the average of the x values obtained will be close to E[ X ] . C ENTRE OF M ASS : when there is a particle of mass p X ( x ) at each location x . B ETTING P RICE : E[ X ] is the fair ticket price for a game where the player wins amount x with probability p X ( x ) . Note that the last two interpretations mainly apply to discrete random variables. N OTE : The expected value of a discrete random variable is not necessarily the most likely value. It may not even be a possible value....
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Lecture18 - DSAP NUS Semester 1 2008/2009 – 146 L ONG-R...

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