# Question

Show that X is stochastically larger than Y if and only if

E[f(X)] ≥ E[f(Y)]

for all increasing functions f .

Show that X ≥st Y, then E[f(X)] ≥ E[f(Y)] by showing that f(X) ≥st f(Y) and then using Theoretical Exercise 7.7. To show that if E[f(X)] ≥ E[f(Y)] for all increasing functions f, then P{X > t} ≥ P{Y > t}, define an appropriate increasing function f.

E[f(X)] ≥ E[f(Y)]

for all increasing functions f .

Show that X ≥st Y, then E[f(X)] ≥ E[f(Y)] by showing that f(X) ≥st f(Y) and then using Theoretical Exercise 7.7. To show that if E[f(X)] ≥ E[f(Y)] for all increasing functions f, then P{X > t} ≥ P{Y > t}, define an appropriate increasing function f.

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