how to understand the equation in pic?

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X is a discrete random variable.
x is any value it can take.
In xεX below the ∑, X is the set of possible values for x.
Regards

Z
 

X^n represents a sequence, and x^n seems to do the same thing, what is the difference?
 

X is a random variable that takes discrete values each of discrete probability(Xi--->PXi). So to calculate the expectation of g(X) yo should make the sum of all possible values of g(X) multiplied by their correspondent probabilities. here x represent Xi for each step of the sum.
 



thanks all,

i think i got it
 

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