Hi I would appreciateany help! Thanks :) Let (,F, P) be uniform distribution on

Question

Hi I would appreciateany help!
Thanks :)

Let (,F, P) be uniform distribution on = {1, 2,3}. Find random variables
X, Y,Z on (,F, P) such that P(X > Y )P(Y > Z)P(Z >X) > 0 and E(X) =
E(Y ) = E(Z). Hi I would appreciateany help!
Thanks :)

Let (,F, P) be uniform distribution on = {1, 2,3}. Find random variables
X, Y,Z on (,F, P) such that P(X > Y )P(Y > Z)P(Z >X) > 0 and E(X) =
E(Y ) = E(Z).

Explanation / Answer

Let X, Y and Z have the same uniform probability distribution(i.e., P(X=1) = 1/3 = P(X=2) = P(X=3)). Then P(X>Y) = P(Y>Z)= P(Z>X) = 1/3 (the first two equalities, by symmetry). So theirproduct is 1/27. And since the probability distributions are thesame, they must have the same expected value (=2).

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