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In the general case, you'd take whatever formulas you have for return rate and corresponding probability (e.g. exponentially lower chances of exponentially higher returns), and feed that into a definite integral from -infinity to infinity (0 to infinity in the case of a model like investment return rate where you theoretically can't lose more than you put in). Consider, for instance, that the area under a standard normal curve (like any probability distribution) is 1, yet that curve extends infinitely in both directions, and there's a non-zero chance of it producing an arbitrarily large value.

If you have a continuous analytic model, you can integrate that analytically (or for the various standard models, just look up the answer based on the parameterization). If you have a discrete analytic model (a step function), you can construct an infinite series. If you have a model based on discrete statistical samples and extrapolations thereof, you can use a combination of numeric integration/summing and model-based bounds.

So, even though the total possible return on a business venture is potentially unbounded, you can still establish a finite expectation value for it.



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