Question: Let X and Y be two random variables distributed on [a, b], with distribution functions F and G respectively. Assume that X FOSD Y .

Let X and Y be two random variables distributed on [a, b], with distribution functions F and G respectively. Assume that X FOSD Y . (a) Show that E(X) E(Y ); (b) Note that this does not mean X Y. To see this, let X be uniformly distributed on [0, 1]. Let Y = 1 X . Show that X is FOSD but XY does not hold.

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