Question

if Y<=X, then
E(Y)<=E(X)
proof???

Answer 1

If i tell i know the proof then

Answer 2

The theorem assumes that X and Y are defined on the same probability space Ω. X≤Y means X(ω)≤Y(ω),∀ω∈Ω. Actually, it would be enough to have X(ω)≤Y(ω) for P-almost all ω∈Ω, where P is the probability measured

Answer 3

it's not true
for instance :
y= 0.2
x=0.3
E( ) = -X^2
E(Y)=-0.04
E(X)=-0.09

here Y<=X but E(Y)>=E(X)