Close. But we can’t all seem to agree on what that means. I’m going to assume that A means your envelope, B means the “other” envelope, and X means th...
To what purpose? It doesn't help you to answer any of the questions. Besides, the correct expectation formula is /(P1 + P2), where P1 and P2 are the p...
This is only true if we do not look in an envelope. That *is* the OP, but the other has also been discussed. It is true because we only need to consid...
Certainly. It isn't "objective." I thought I made that pretty clear. Before I say whether I agree with the value, you should understand that "pick at ...
This emphasizes how a probability space changes based on your knowledge. Or rather, what knowledge is missing. I just flipped a coin on my desk. I can...
Well, I can't address your disagreement unless you explain why you feel that way. That characterization is correct. There may be different ways people...
The highlighted assertion is incorrect. First off, "objective probability" means the "likelihood of a specific occurrence, based on repeated random ex...
So, you are willing to risk losing $5 for the chance to gain $10? Regardless of the odds behind that risk? Say I offer you the chance to play a game. ...
Why? I think you confuse the fact that probabilities are intangible with being unreal. Probability is, essentially, a measure of our uncertainty about...
I did read the thread. You did not read my replies. Like this one, where I said "you have no information that would let you calculate " and you replie...
But we do know that it can't be true. That's the point. Either can't be true for all values of this "a", or there are impossible values in the set of ...
I have agreed that what you said near the beginning of this thread was right. Did you read that? You have been very reticent to point out what it is y...
You have not interpreted a single thing I have said correctly; in fact, you've replied to very few of them. Most significantly this time, how Bayesian...
From Wikipedia: Since there is no provision for "data/information/evidence" in the OP, only a one-time thought problem, Bayesian inference does not, a...
But the probabilities are not the same as the probabilities of having picked the larger, or smaller, value. They are the probabilities of picking the ...
So an "uninformative prior" is not a "prior" ? And an informative prior that is based on only partial information is not still a "guess" about the res...
And that unknown value in his pocket has a distribution. We don't need to "check it," as long as the symbolic probability space we use satisfies the r...
Jeremiah oversimplifies. If you use a specific distribution, then your results apply only to that distribution and not the OP. And AFAIK nobody but Je...
No, it gives you a strategy that works on your assumed prior, not necessarily on reality. The point of a Bayesian analysis is to guess at a prior, and...
I agree. I think it is most convincing to present multiple angles. But it isn't (just) the sample space that is the issue. It is the probability space...
Of course you won't. You don't like facts that disagree with your beliefs. You have made various claims in this thread, I've told you which you are ri...
I hope I'm not talking down, that isn't my point. But probability really needs great care with terminology, and it has been noticeably lacking in this...
If you did, that statement was completely obfuscated by your sloppy techniques. And it isn't the argument that is flawed, it is the assumption that yo...
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 again, you won't say what results you mean. Your solution from page 1, that ... ... is a correct solution to the original problem when you don't l...
The point is that there must be a prior distribution for how the envelopes were filled, but the participant in the game has no knowledge of it. I expr...
If you want to address the original problem, it matters that by your methods, ignoring their other faults, the two envelopes can contain the same amou...
Use a "ceiling" function instead of a "round" function. Or just add 0.0005 before you round. Any statistical analysis addresses a question. Yours addr...
Right. That was after my first post. I read it before the rest of the thread, so I didn't think that was what you were referring to. I didn't want to ...
I did look. Maybe you didn't read mine: "I mean examples where actual envelopes have been filled with actual money, and presented to an actual person....
Sorry, I don't know MathJax. With having broken my foot on Friday (did you notice a gap in my responses?), it is taking all the effort I can spare to ...
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 cou...
I've looked at them all,and seen no actual data. By which I mean examples where actual envelopes have been filled with actual money, and presented to ...
Mixing random variables and unknowns can be very un-intuitive, especially to those who are out of practice. That isn't as useful as you might think. Y...
But I have read it now - the majority is either name calling, or the debating of INCORRECT interpretations (on almost all sides) of various concepts i...
What? You don't want to address a correct analysis, until I weed through pages of debate that appears to be inconclusive? Because I can guarantee you,...
Yes, my point was that the lottery example is a very bad description of a sample space. In fact, It is the archtype for just that. But so is ignoring ...
Imagine three variations of this game: Two pairs of envelopes are prepared. One pair contains ($5,$10), and the other pair contains ($10,$20). You pic...
But she isn't asked for her confidence in that situation, so this argument is a red herring. A very appealing red herring, as you go on to describe, b...
No, it isn't. Statistics is about expectations. Statistics uses Probability Theory to calculate expectations. In conventional experiments, we find tha...
Yes, it is. The bolded text tells the lab techs what to do - or more accurately, what not to do - on both days. It defines two protocols for TAILS: in...
This is incorrect. What happens on Tuesday&HEADS is a part of the HEADS protocol, so you excluded part of it. And you treat the various possibilities ...
It is indeed true that Beauty has no evidence that she can use to distinguish Monday from Tuesday. This does not mean that such evidence does not exis...
Demonstration of concept #1: Beauty is put to sleep on Sunday, as in the original problem. Then a single, fair six-sided die is rolled. Based on its r...
Four Beauties volunteer to undergo the following experiment and are told all of the following details: Four cards have been prepared; one says "You wi...
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