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Understanding the Equation of Monte Carlo Method returning value to the expected function

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I was reading an article related to MonteCarlo Method. The link of the article is:



I found the equation in the following attached image. 

1)In the equation related to the attached image, we are assigning a value to a function. What does this mean?

2)What the expected function will do with this value?

3)Please guide me by providing examples of function fX(ꭓ), E(g(X)) and g(ꭓ).



MonteCarlo Equation1.jpg

Edited by zak100
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The statement is a little confusing.  I believe its intent was to consider only those values of X which have a probability greater than zero.

Simple example: X has 3 values 0,1,-1. f(-1)=1/4, f(0)=1/2, and f(1)= 1/4.  g(-1)=0, g(0)=1, g(1)=2.  Then E(g(X))=1.

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