If, at that point, you postulate a value in an envelope, you need to postulate a probability distribution that covers all possible ways that value could be in an envelope. Even if it is unknown. — JeffJo
Did you miss the part where I said — JeffJo
In short, the "need to" include the probability distribution is because the formulation of the "simple algebraic solution" is incorrect if you exclude it.I'm just trying to understand the "need to" in that sentence.
I am well aware 0 was a possible outcome, the code just runs better without the loops, and it was not significant enough to care.
Sorry my simulation proves you wrong.
some knowledge of the bounded probability distribution of the possible contents of the two envelopes — Pierre-Normand
I'm having trouble imagining what the source of this knowledge might be. — Srap Tasmaner
And again, you won't say what results you mean.I am happy with my correct results.
... is a correct solution to the original problem when you don't look in the envelope. The problem with it, is that it doesn't explain to why his program doesn't model the OP. That is something you never did correctly, and you refuse to accept that I did.If you have X and you switch then you get 2X but lose X so you gain X; so you get a +1 X. However, if you have 2X and switch then you gain X and lose 2X; so you get a -1 X.
... is also correct, although it is easier to prove it directly, But it is still irrelevant unless you determine that the two distributions are independent. AND THEY ARE NOT.the possible distribution of A is the same as the possible distribution of B
... that is incorrect, as I just showed in my last post. The probability that A has the smaller value depends on the relative values of two probabilities in that distribution, so it is significant to the question you address here.the distribution in which X was selected from is not significant when assessing the possible outcome of envelope A and B concerning X or 2X.
It is provable without simulation that the the two distributions are the same, so this is pointless. We can accept that the distributions are the same. And it is is obvious you didn't read my posts describing why the simulation is pointless. In short, the "data" you apply "data science" to pertains only to how well your simulation addresses the provable fact.The point of this demonstration is to show that the possible distribution of A is the same as the possible distribution of B. ... So we see with a D test statistics of 0.0077 and a 0.92 p-value we don't have strong enough evidence to support the alternative hypothesis that the two distributions are reasonably different.
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.