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


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Hi,

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

http://ib.berkeley.edu/labs/slatkin/eriq/classes/guest_lect/mc_lecture_notes.pdf

 

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).

 

Zulfi.

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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