how to understand the equation in pic?

[W_Heisenberg]

what does x and X mean? also the alphabet "x", what are these things?

 

[zorro]

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

 

[W_Heisenberg]

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

 

[zorro]

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

In the picture you posted there are not any X^n nor x^n.
Can you clarify?

Z

 

[Fadi Mkhayel]

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.

 

[W_Heisenberg]

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