Show that X is stochastically larger than Y if and only if E[f(X)] E[f(Y)] for all
Question:
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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Suppose X st Y and f is increasing Then PfX a PX f 1 a PY f 1 a ...View the full answer
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