a quantity that takes any of a set of values with specified probabilities.
a quantity that may take any of a range of values, either continuous or discrete, which cannot be predicted with certainty but only described probabilistically
Collins English Dictionary - Complete & Unabridged 10th Edition
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The tendency for subsequent observations of a random variable to be closer to its mean than the current observation.
Standard deviation has to do with measuring the variation in a random variable.
You're treating the amount of money in the second envelope as a random variable, where it is not.
The standard deviation is a measure of the variability of the distribution of a random variable.
Skewness is a measure of the departure of the distribution of a random variable from symmetry.