How many moments are needed for a discrete distributions I am doing a project on imaging and I have a more general question about imaging. 

In general we use the moments of the distribution of the object imaged, because the capture information about the image. If our image is continuous then we will need in general infinite number of moments to describe it correctly. (Because if we consider the image as a function and we take the Taylor expansion in moments we will need all of them).

My question is, if we have a discrete distribution, 2 or 5 points that we want to image, how many moments do we need? Do we still need infinite of them or just 2 or 5?

Thank you!
You can do $E\{ x^n \}$ as much as you want. How much is necessary is up to you but the unique characterization of a distribution is not the same thing as a cutoff point of a moment expansion.  Some distributions can be very compact with respect to their moments but others are not.  My experience is that moment (taylor like) expansions can converge very slowly. 

For something like a binomial distribution, all I need to know to represent the pdf is $p=$ success and know that the trials are independent.   The probability density for successes given a number of trials flollows from the mathematical formula.