Let me try rewriting this.

Your sample space is [R =L/2, R = 2L].

Which means your distribution here:

= P(R=5 | L=10)(R) + P(R=20 | L=10)(R)
= R

Could be:

= P(R=5 | L=10)(R) + P(R=20 | L=10)(R)
= L/2

Or

= P(R=5 | L=10)(R) + P(R=20 | L=10)(R)
= 2L


Let me think about it some.

-----

Thoughts in progress. . .

= P(R=5 | L=10)(L/2) + P(R=20 | L=10)(2L)

Sorry, but I need more clarification on where you are going with this.

I agree, it was not very thought provoking.

The error here is making new assumptions upon seeing Y.

The pro switchers never really gave a good reason how to reconcile the fact that their model has the potential to make impossible predictions. That is a valid reason for concern and if a model which makes no new assumptions upon seeing Y only provides possible outcomes then that is a definitive reason to favor that model.

Until they fix that problem, that will stand against their methods of approach.

I mostly use R, and am toying with Python in case that turns out to be useful if I want to get into 'data science' — andrewk

There is no reason to put data science in quotations; it is a real branch of modern science.
The advancements of computers and the age of big data is what created a need for specialist in analyzing data.The two most common forms of data scientists are statisticians and computer scientists; however, there are other flavors as well.

R is mostly used by statisticians for data analysis, my impression is that Python is mainly used in machine learning, which would be the computer science side. From what I have read, it is not too hard for a statistician to cross over into machine learning, as many of the machine learning concepts come from statistical theory and practice. If your goal is simply to engage data analysis, and you already know R that is well enough, and more preferable if you wish to go the statistics path. However, being a statistician requires that you know both Classical and Bayesian methods, as many of the model assumptions in Classical statistics persist over into Bayesian statistics.

I did not say you have full knowledge. All of the concerns you are expressing have already been addressed by multiple people multiple times, and I don't feel like going in circles over this any more.

I summed this up towards the start of the thread:

You have two envelopes, A and B.

There are two possible amounts for the contents of the two envelopes either X or 2X. You don't know which is which.

We'll call amount X case R, and and amount 2X case S.

You are handed envelope A.

Before you open it, you know that A could be case R or it could be case S. You have no clue which it is, so as an uninformative prior you give each case a 50% likelihood.

Now for the tricky part, you open envelope A and see it has 10 bucks in it.

Intuitively this seems like new information which would call for you to update your prior; however, it still does not tell you if are you in case R or case S. You don't know if that is 10=X or 10=2X. So in truth you can't really update your prior, as your prior was based on the uncertainty of being in case R or case S.

So your prior stands.

You consider swapping. You look at envelope B and realize it could be in case R or case S. You don't know which, so just as before you give it an uninformative prior and you give each case a 50% likelihood.

Now you could swap, but really probabilistically it changes nothing as your initial uncertainty would still stand. You would just trade the uncertainty of A for the uncertainty of B which is the same uncertainty. And the math? Well the math is indifferent to all options. So the decision to swap really comes down to if you feel lucky or not. — Jeremiah

He is also capable of shooting laser beams from his eyes and eating an entire cheeseburger in a single bite.

His speeches make much more sense if you are drunk.

Then how did it get deleted?

That line has been removed multiple times, and there is other missing content. I get removing the remarks you find too abrasive; however, this is not the only content being removed. I have the un-refreshed page on my laptop, right now. It is not there, and I know it was there before I went to bed last night, as I added it back after it was removed.

If you say a mod is not doing it, then you have a problem. A problem which may not be local to just me. Does your log should all edits or only the last edit?

If you continuously re-add stuff that was modded out you'll obviously end up getting banned. — Baden

I actually don't care much if I get ban. If I did then I won't act the way I do.

But does the reasoning make sense? — Dawnstorm

It makes sense, but it is wrong, and that is why it is misleading.

Forget the math and just think about this rationally.

Consider:

I have two envelopes and I secretly put 10$ in one and 20$ in the other, then hand you one at random.

You open it and see there is 10$. You have no idea what is in the other envelope so you imagine it could be 20$ or it could be 5$. However, it can't be 5$ ever, as it is 20$. A 5$ outcome would be impossible, so your imagination is feeding you false information. You imagined a number that is not even a possible outcome.

The distributed amounts into the envelopes is X and 2X and it will always be X and 2X no matter what you imagine it might be or how much you know about the envelopes.

Also, all this has been covered in extensive depth.

The problem with the [5,20] argument is that one of those numbers is not possible, therefore calculations based on those numbers will be misleading. To do so is to incorporate false information into your math.

you're defining the envelopes according to "contains 2X [10,20]", "contains X [5,10]". — Dawnstorm

Sorry no, that was not my intent. In the event of R you have A=10 and B=20. In the event of S you have A=10 and B=5. These are mutually exclusive events, which means in the case of R the amount 5 does not exist at all, and in the event of S the amount 20 does not exist at all. So one of those sample spaces is feeding you false information. The only way to avoid this is to treat X as the unknown variable it is.

Here was the original argument, which I only did because Michael requested that I do it. However, an algerbic solution, which I have posted several times already, models this problem much more accurately.

So we have two cases here and have no clue which one we are in. Earlier I defined these cases as amount X case R, and and amount 2X case S. We have a lot of variables flying around so let's try to be consistent here.

Now that we have listed all possible outcomes we can define our sample space as [R,S], well call this sample space 2.

Now remember by our definitions an event is a subset of our sample space.

In event R X=10 and since in event R B must be 2X then B = 20.

So the sample space of event R is [10,20].

In event S 10=2X and since in event S B must be X then B= 5.

So the sample space of event S is [5,10]. (order does not matter)

So our sample space, which we named as sample space 2, is [R,S] where R is the set [10,20] and S is the set [5,10] or we can express it as [[10,20],[5,10]] — Jeremiah

We define A and B as: If A=Y=X then B=2X or if A=Y=2X then B=X, where Y is the amount you see opening envelope A and X is the unknown amount originally selected by the facilitator.

My claim is then that the only possible outcomes for B is X or 2X.

Proof:

For all of Y, Y is a positive real number, such that Y=X or Y=2X, where X is some positive real number.

You are handed A and you see Y inside.

There are two cases here:

Case One

A=Y=X

By definition of A and B if A=Y=X then B=2X therefore B=2X

Case Two

A=Y=2X

By definition of A and B if A=Y=2X then B=X therefore B=X.

Those are the only two possible cases for B therefore by the definition of a sample space the sample space for B is [X,2X]

We define A and B as: If A=Y=X then B=2X or if A=Y=2X then B=X, where Y is the amount you see opening envelope A and X is the unknown amount originally selected by the facilitator.

My claim is then that the only possible outcomes for B is X or 2X.

Proof:

For all of Y, Y is a positive real number, such that Y=X or Y=2X, where X is some positive real number.

You are handed A and you see Y inside.

There are two cases here:

Case One

A=Y=X

By definition of A and B if A=Y=X then B=2X therefore B=2X

Case Two

A=Y=2X

By definition of A and B if A=Y=2X then B=X therefore B=X.

Those are the only two possible cases for B therefore by the definition of a sample space the sample space for B is [X,2X]

We define A and B as: If A=Y=X then B=2X or if A=Y=2X then B=X, where Y is the amount you see opening envelope A and X is the unknown amount originally selected by the facilitator.

My claim is then that the only possible outcomes for B is X or 2X.

Proof:

For all of Y, Y is a positive real number, such that Y=X or Y=2X, where X is some positive real number.

You are handed A and you see Y inside.

There are two cases here:

Case One

A=Y=X

By definition of A and B if A=Y=X then B=2X therefore B=2X

Case Two

A=Y=2X

By definition of A and B if A=Y=2X then B=X therefore B=X.

Those are the only two possible cases for B therefore by the definition of a sample space the sample space for B is [X,2X] — Jeremiah

Jeremiah
1k
We define A and B as: If A=Y=X then B=2X or if A=Y=2X then B=X, where Y is the amount you see opening envelope A and X is the unknown amount originally selected by the facilitator.

My claim is then that the only possible outcomes for B is X or 2X.

Proof:

For all of Y, Y is a positive real number, such that Y=X or Y=2X, where X is some positive real number.

You are handed A and you see Y inside.

There are two cases here:

Case One

A=Y=X

By definition of A and B if A=Y=X then B=2X therefore B=2X

Case Two

A=Y=2X

By definition of A and B if A=Y=2X then B=X therefore B=X.

Those are the only two possible cases for B therefore by the definition of a sample space the sample space for B is [X,2X]

------

Notice how that is for all of Y. A very important concept. Also notice how it says "where X is some positive real number." It absolutely does not matter how X was selected. — Jeremiah

We define A and B as: If A=Y=X then B=2X or if A=Y=2X then B=X, where Y is the amount you see opening envelope A and X is the unknown amount originally selected by the facilitator.

My claim is then that the only possible outcomes for B is X or 2X.

Proof:

For all of Y, Y is a positive real number, such that Y=X or Y=2X, where X is some positive real number.

You are handed A and you see Y inside.

There are two cases here:

Case One

A=Y=X

By definition of A and B if A=Y=X then B=2X therefore B=2X

Case Two

A=Y=2X

By definition of A and B if A=Y=2X then B=X therefore B=X.

Those are the only two possible cases for B therefore by the definition of a sample space the sample space for B is [X,2X]

------

Notice how that is for all of Y. A very important concept. Also notice how it says "where X is some positive real number." It absolutely does not matter how X was selected.

But it's also clear to me there's a conceptual muddle in the argument for switching in the non-iterative case, so I can't get past that. — Srap Tasmaner

There is no point in even approaching probability and expected returns without properly defining the sample space. As if that is not right, the rest of it won't be right.

You claim the sample space is [5,20]

The sample space is defined as all possible outcomes, but for 5 to be a possible outcome then 20 must be an impossible outcome. For 20 to be a possible outcomes 5 must be a impossible outcome. Therefore by the definition of a sample space your sample space cannot be [5,20].

Expect for one to be possible the other one has to be impossible and therefore can not be included in the same sample space as possible outcomes. R and S are mutually exclusive events.

This is a rerun. . . .

R and S are mutually exclusive events.

It's a meaningless question. 'on average' is not a meaningful statistical concept. We can only meaningfully talk in terms of expected values. The expected values depend on the distributions of the random variables, and those distributions will depend on the information available to the person that is forming the expectation. — andrewk

The definition of a statistic is. . . .

A statistic is any quantity that can be calculated from the observed data.

. . . the word mean when referring to an average calculated over an entire population. A mean is therefore a parameter. When referring to the average in a sample--which is both a statistics and estimate of the population mean--. . .

The Statistical Sleuth, A course in Methods of Data Analysis. By Ramsey/Schafer

The expected value of a random variable is just the mean of the random variable. — Statistics How To

.

As described in the post immediately above, that setup does not reflect the player's knowledge and expectations. — andrewk

None of us has yet to actually play this game; as such, we reflect the player's knowledge and expectations.

I'm learning as I go here. — Srap Tasmaner

These are the lecture notes from one of my professors, which should give you some idea of what Bayesian statistics is suppose to look like.

http://www.math.montana.edu/ahoegh/teaching/stat491/notes/index.html

Given what we know, as it stands, the evidence leans in favor of freedom of choice.

You tell me.

Holy crap! Trump is the president. We are all doomed!

The stress is subjectivitaly beinging put on the word the, and that stress is ambiguous. This is a grammar issue, not one of logic.

I have a saying I came up during my decade in customer service.

People are people are people are people . . .

I estimate that during that period I spoke one on one with roughly between 150k - 170k different people from all over the world, of all types and ages. I learned that they are all same, all of them. I also think that humans were never meant to mass interact on that level, it left me with with a general dislike of people. I quit before that dislike grew into something more, but I still have a hard time not getting irritated with just about everyone.

But what to do stats on? What counts as significant? What about necessity as opposed to contingency? What do the results mean? Why does it matter? And some things are not amenable or appropriate for statistics. It is subsumed in philosophical meta-analysis and theories of value, significance, and what is the case. — schopenhauer1

It is subsumed in science, literature, history, politics, art, etc. . . . They all do it, all by themselves.

Also, if "philosophy" is part of every other discipline, then we don't really need it as its own separate entity.

You are not bringing anything unique to the table.

You can't prove free will until you disprove fairy magic.

You can't prove free will until you disprove mind control Sun spots.

You can't prove free will until you disprove that this is a computer simulation.

You can't prove free will until you disprove <insert any random crap>.

Using unfalsifiable claims as the standard of proof is just thoughtless and leads nowhere.

I understand that if one lowers the standard to "empirical" evidence one can prove/disprove free will but I'm looking for a sound deductive argument to deal with the issue of free will. — TheMadFool

Exactly how I am lowering the standard of empirical evidence? Freedom of choice is empirically demonstrable and your statement here is just a hollow facade. You need to give a real reason as to why this evidence should not be considered.

Anyway, I'm saying we can't prove free will exists not that we can't disprove determinism. — TheMadFool

You are trying to use determinism, an unfalsifiable claim as the standard of proof for free will.

In your own words. . . .

I think you have the science wrong. — TheMadFool

You can't use an unfalsifiable claim as the standard of proof. Now, I am sure like all "philosophers" you think this is a matter of interpretation, opinion or whatnot; however, it is not. What you are demanding amounts to arguing that if one cannot disprove fairy magic then we can't really know if gravity is a force that attracts objects with mass.

So your arumgent is that since we cannot disprove determinism then we cannot prove freewill.

That is an impossible standard. I also cannot disprove fairies or unicorns. However that neither proves or disproves their existence.

Determinism is what is known as an unfalsifiable claim, it cannot be proven or disproven and consequently cannot be used to prove or disprove, as you don't know if it is real.

On the other hand we can empirically demonstrate freedom of choice.

So given your unfalsifiable claim vs. empirical evidence, I'd say the evidence has a lot more weight and creditability.

I am a student of statistics, a data science. You are literally describing data science, which spans into all fields, including philosophy.

Hating takes to much effort and is a poor use of your time and energy.

As such, I reserve hate only for loved ones, as they are the only ones worth that level of effort. However, I will regulate annoyance and frustration to lesser concerns.

It is an emotion, which is considered intersubjectivally verifiable, or in other words you need to relate to his expression on an empathical level.

I don't think this has anything to do with logic, and this is posted in the wrong section.

One of the big things philosophy can provide is systematic thinking AND understanding systems — schopenhauer1

We don't actually need philosophy for that, as that is not unique to philosophy. I would even argue that there are other academic areas that do a better job at setting one for systematic thinking and comprehension.

Think: How much porn do humans produce?

Maybe it's the meaning of life.

How to you square the galaxy-spanning deity with the same god having a detailed interest in your penis-related activities? — Bitter Crank

God created us so he'd have some porn to watch.