You have two functions. The first returns an integer between zero and ten, while the second returns any real value between zero and ten. If you get paid based on whatever value is returned, which payoff function would you rather have?
I am looking at this question that trading companies sometimes ask, and I understand the expected value for both is 5, but the variance for the 1st is 27/2> 25/3 which is the variance for the 2nd.
Is there any other consideration. If not I presume investors pick investments that have the same expected value with lower variance, so would be inclined for the uniformly distributed returns.
I am actually interested generally, as from my primitive understanding, the proposed variance and expected value, and other moments, are surely the main thing that drives an investment decision.