swh, thanks as always for your informative and practical reply, in this case a yr6 maths lesson.
So I design a new engine and put it onto a new aircraft, I should be able to get ETOPs, because the MTBF would be zero until the engine failed (as you cleverly pointed out, anything multiplied by zero is zero

)
But didn't you say;
At design phase there is a theoretical constant MTBF
so then, in your own words, these engines x would have a MTBF other than zero, so do the maths again using any number other than zero for the silly scenario.
Now a serious question on the MTBF formula;
I don't pretend to know much about it, but could you clarify it for me. From what you're saying different operators must have different MTBF's. Is the following then correct?
MTBF = (flying hours*aircraft quantity)(of that operator)/(number of confirmed failures)(of that engine worldwide)