When all I said was that any use of statistics - which you did advocate repeatedly - — JeffJo

Statistics is simply not designed for a problem like this; it is better to just use basic mathematics. Statistics is for analyzing data. — Jeremiah

This is me on page six. You are grossly mistaken on this point, never once did I advocate the use of statistics for addressing the OP. I talked about statistics in response to others but I was very vocal and clear that it should not be used for the OP. Had you read the thread you would have known this and been able to place my posts concerning statistics in proper context.

The solution has always been what I posted on the first page of this thread in post number 6, which has also been my stance this entire thread. A statistical solution has never been a viable option, which has also been my stance this entire thread. The truth is this problem has always been really simple to solve, it is untangling all the speculations and assumptions that confounded it.

The limit does not need to be specified, as the envelopes will never step outside the limit. Mathematically you cannot determine if you have the the smaller amounts or larger amounts as you can never rule out which case you are in. You can speculate on such things, but you can't quantify them. It is pointless to consider the conditional probability since both cases are subjectively equal in probability, it would still boil down to a coin flip. You can do it for completeness, but it really makes no difference.

you became belligerent started saying you would not read anything I wrote until I had read all of the irrelevant posts. — JeffJo

And yet you didn't read the posts, did you? Not then, maybe you read a few more after I pushed you. I may be an ass, but at least I read a thread before criticizing people.

The point is that there must be a prior distribution for how the envelopes were filled — JeffJo

True, but you will have no knowledge of what that may be.

it gives you a strategy that works on your assumed prior — JeffJo

Assuming your prior is correct, that is.

Then go ahead and switch envelopes in the OP. — JeffJo

There is not enough information to calculate expected gain.

You people really need to drop this Classical v. Bayesian mind set many of you have. The idea that they are somehow different tool boxes is misleading, they come from the same tool box.

I very specifically want to know why you need me to go first, when I asked for your thoughts.

Who is Richard Dawkins?

Is it just me or did @raza just admit he is poorly informed when it comes to our President?

Why you have to work through his history? Do you not stay informed about the President?

Would you say the same about other things we once did not know the nature of, such as disease, or neurology? I'm not sure if the nature of the invisible pink unicorn is knowable or not, but wouldn't it be irresponsible to remain willfully ignorant? Also, according to Pascal's wager wouldn't it be more intelligent to behave as if a invisible pink unicorn does exist?

Invisible Pink Unicorns are beings of great spiritual power. We know this because they are capable of being invisible and pink at the same time. Like all religions, the Faith of the Invisible Pink Unicorns is based upon both logic and faith. We have faith that they are pink; we logically know that they are invisible because we can't see them.

— Serah Eley

When you all get together and agree on what "God" is, ask me again.

Statistics is used on an experimental data set from repeated trials. — JeffJo

Yes, and it is also used on observational data sets to make generalized inferences about a population.

How could anyone who has read this thread possibly concluded I was ever advocating for a statistical solution. I have been very clear that a statistical approach is incorrect.

So Sessions is all you have? You can't think of anything else at all?

... [Y]ou have been misinterpreting me since you joined the conversation. ...

It is telling how hard @raza has to work to find any faults at all with President Trump. My guess is that he has to run it though his supervisor before getting approval to post.

So you are faulting his lack of action. Can you find fault in any of his actions?

Give me a specific mistake that Trump HAS made.

What specifically are these mistakes you are talking which Trump has made as President.

Either way, you have made it your job to troll for Trump. You won't criticize President Trump at all, you have admitted to that.

I am thinking that you are not allowed to criticize Trump. The idea that he is perfect and has not made any mistakes at all, is just too far out there, even for you.

Plus it is what you are being paid to do.

It is completely nuts that you can't bring yourself to criticize one fault. If you are not able to see his errors, then clearly you are not able to view the man objectively. Even the most die hard Trump fan should be able to see that man makes mistakes. Maybe your employer doesn't allow you to post criticisms of Trump.

If God exist you should going on living as if God does not exist as you are still clueless to the nature of God.

I was never the one advocating for the use of a prior. I am not sure where you got that notion.

So you are completely incapable of seeing any faults in the President.

I have also already shown that trying to calculate expected returns is a misguided effort.

My simulations were there to display the inherit ambiguity in defining a prior distribution. X is an unknown, treat it like an unknown. I have never once in the entire thread expressed that there is no limit or distribution, in fact I expressed the opposite. That doesn't change the fact that X is an unknown.

Can't even think of one?

The subject has been mostly this russia conspiracy theory. — raza

You make it that way, Raza.

Trump's flaws is that he is probably a fairly complete narcissist. — raza

That is dodge.

Give a specific error he has made.

I ran across this line while reading one of my books and thought it pertained well to this thread:

The final criterion for deciding whether a model is "good" is whether it yields good and useful information. The motivation for using mathematical models lies primarily in their utility.

Mathematical Statistics with Applications, Wackerly, Mendenhall, Scheaffer.

I will let people interpret that in the context of the thread how they like.

Personally, I think in terms of modeling the actual OP the inclusion of distributions or switching strategies is misguided. If our goal is to assess the situation before us then they move outside that scope. However, these models do provide a useful platform to investigate properties that may be applied to other probabilistic aspects. I know undoubtedly some will take that to mean something I don't mean, but there is not much I can do about that.

Somehow I will live with the loss. It will be hard, but I will push on.

All you do is assume, Raza. This entire thread is just you spitting out baseless assumptions and wild fantasies. Always in favor if Trump, but surely you can't think the man is perfect, right? There must be some flaws.

Yes, the poor oppressed conservatives . . . . :roll:

And what if angels decent from the sky and crown Trump ruler for all time?

I don't care about your fantasies, Raza.

In nearly every public opinion poll Trump's support stems almost exclusively from the Republicans, and the number of Americans voters who identity as Republicans or leaning towards is shown to be lower than those who identify with the Democrats in the most recent polls that I cared to look at. If you can find a more current and legitimate poll I am all for it.

Forty-four percent of U.S. adults identify as Democrats or are independents who lean to the Democratic Party, while 37% are Republican identifiers or leaners. Democrats have maintained an edge of between five and nine percentage points on this measure of party affiliation throughout 2017, after holding a narrow advantage in late 2016.

https://news.gallup.com/poll/223124/democratic-party-maintains-edge-party-affiliation.aspx

This is USA history repeating itself, Raza. The sitting president always motivates opposition to his party. If you think the majority is going to ride in on a white horse to save Trump then you are fooling yourself, as at the very least, half of America thinks Trump is a shithead. You don't need polls to figure that out, it is just common sense.

Of coures it is the public's perceptions. Did you already forget that you were talking about how the public views this. I am addresing your misconceptions on that point.

The feminization of the left has made them vulnerable to the soap opera fantasy that the main stream media is putting out as news. — wellwisher

Did you just suggest that women are more gullible than men?