No worries, I think your solution coverges with @Someone's above, if I am not mistaken. You're multiplying the probabilities for all values of j up to i for all values of i.

Yes I am and yes I think it does:

edit - actually, the calculations from the other guy are probability calculations, so this is related to the median. I have given you a mean calculation, which should be related to the average. But you already mentioned that they are close ...