Regarding the phenomenon we watched in Section 1.2.4, discuss to what extent the situation changes if we replace in (1.2.2) the standard deviation by the variance. In particular, consider the situation of Exercise 7.

Exercise 7

Let X be uniformly distributed on [0,1], and let Y take on values from [1, ∞), and P(Y > x) = 1/x^α for all x ≥ 1 and some α > 2. This is a version of the Pareto distribution we discussed. Verify that

Show that though P(Y ≥ X) = 1, for α sufficiently close to 2, Y is worse than X under criterion (1.2.2).