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A distribution is a mathematical description of probabilities or frequencies.
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Expectation of a Random Function
expectation:-
E[f(x,y)]..... x
Where
f(x,y) = y if (x-y)>0
f(x,y) = x, if otherwise
The way I was thinking is
E[f(x,y)] = yP((x-y)>0) + x(1-P((x-y)>0))
P((x-y)>0 is something I can compute from the distributions …