Expected Value Function

An Expected Value Function is a mean function that returns a random variable's expected value.

• AKA: E.
• Context:
  • range: Expected Value.
  • It can be created by an Expected Value Function Creation Task.
  • …
• Example(s):
  • Let X be a discrete random variable with pmf pX(x) and support S_X. The expected value of X is given by E(X) = X x∈SX xpX(x). (Dubnicka, 2006c).
  • …
• Counter-Example(s):
  • a Probability Function.
• See: First Moment, Moment Function, Sample Mean, Sample Variance, Point Estimate, Expected Utility.

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References

2015

• http://en.wiktionary.org/wiki/Appendix:Glossary_of_probability_and_statistics#E
  • expectation of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). … The concept is similar to the mean. The expected value of random variable X is typically written E(X) or [math]\displaystyle{ \mu }[/math] (mu).

2006

• (Dubnicka, 2006c) ⇒ Suzanne R. Dubnicka. (2006). “Random Variables - STAT 510: Handout 3." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
  • QUOTE: The pmf of a discrete random variable and the pdf of a continuous random variable provides complete information about the probabilistic properties of a random variable. However, it is sometimes useful to employ summary measures. The most basic summary measure is the expectation or mean of a random variable X, denoted E(X), which can be thought of as an “average” value of a random variable.
  • TERMINOLOGY : Let X be a discrete random variable with pmf pX(x) and support S_X. The expected value of X is given by E(X) = X x∈SX xpX(x).

2003

• Liu, Yian-Kui, and Baoding Liu. “Expected value operator of random fuzzy variable and random fuzzy expected value models." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 02 (2003): 195-215.
  • QUOTE: … … In order to speed up the solution process, we will train a feedforward NN to approximate the expected value function U. We denote the network weights by a vector w. Hence the output of mapping implemented by the NN may be characterized by F(x,w). …

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