EXPECTATION

OF A CONTINUOUS RANDOM VARIABLE

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Expectation (average) of a continuous random variable X is

(Note that this is just the continuous equivalent of the discrete expectation.)



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Another Way to think about Expectation:

Think of a variable mass object on a line. The mass at every point, x, is fx(x). The Expected Value of the random variable is the point on the line where you should put your finger to make the masses balance. This balancing point is also called the centroid.



See SeeSaw Activities by the Calculus group in Project Links for more information on Centroids.

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RELATED
CONCEPTS

  Random Variables
Probability Density Function
Cumulative Distribution Function
Properties of Continuous Random Variables
Expectation of Discrete Random Variables
Important Continuous Random Variables
Arithmetic Mean
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Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.