[This was meant as a comment to Tim's answer, which I liked, but it's too long.]
There's a comment by Rasch along the lines of Tim's answer:
First a terminological remark. The "prediction" is suggestive of the statistician as a magician who can tell the future. Economists have an expression that is less pretentious: forecasting – not much more reliable than weather forecasting.
To speak seriously: you do not really predict anything. What you do, is to calculate the distribution of the variate in question, possibly offering its mean value or the like as a likely event – but only on the assumption that the model – or a characteristic feature of it – on which you based this forecasting, still holds, i.e. confronted with what eventually does happen you are faced with a test of this hypothesis and nothing else – you were not telling what the future would be!
on p. 268 of "Sufficiency, prediction and extreme models" by Lauritzen (Barndorff-Nielsen & al, eds: Conference on foundational questions in statistical inference, Aarhus 1973).