We say that X is stochastically larger than Y, written X ‰¥st Y, if, for all t.
P{X > t} ‰¥ P{Y > t}
Show that if X ‰¥st Y, then E[X] ‰¥ E[Y] when
(a) X and Y are nonnegative random variables;
(b) X and Y are arbitrary random variables.
Write X as
X = X+ ˆ’ Xˆ’
Where

Similarly, represent Y as Y+ ˆ’ Yˆ’. Then make use of part (a).

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X if X0 XX if X<0 0 if X