The standard deviation is inversely proportional to the square root of the sample size. Success may be the result of a positive expectation but can be the result of a standard deviation, where many live in the variance.
if each possible outcome is not equally likely then each must be weighted according to its probability or element of change
if mean vs volatility then mean-variance analysis offers criteria for earning best combination of compound return on investment
The mean-variance analysis is static for given what you know now.
The mean-variance analysis is a theory over time at present frame.
Variance increases along with the arithmetic mean.
Variance goes to zero along with a geometric mean.
if zero is a chance of any outcome then the geometric mean is zero
if a geometric mean is zero then variance does not matter as there is a zero outcome with time
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