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

$$E[f(X)] = E[/(Y)]$$

for all increasing functions f.

HINT: If X, Y, show that E[f(X)] E[/(Y)] by showing that f(X)st f(Y) and then using Theoretical Exercise 7. To show that E[f(X)) E[f(Y)]

for all increasing functions fimplies that P(X) = P(Y > r), define an appropriate increasing function /.