# Question: We say that X is stochastically larger than Y written

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+ − X−

Where

Similarly, represent Y as Y+ − Y−. Then make use of part (a).

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+ − X−

Where

Similarly, represent Y as Y+ − Y−. Then make use of part (a).

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