For Q 10 the easiest way to do it is to recognise that F(x) <= G(x) for all x means that for any x, X takes smaller values less than x is more likely to occur in G than in F. Or in other words, X takes smaller values than x in G more often than it takes in F. So, expectation of X in F must be greater than or equal to expectation of X in G. More formal proof is attached.

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