It's clear you don't understand mine. Nor have you tried. Yes, it is. That is exactly what you have not addressed. And you would be wrong to do so. Al...
And you still haven't grasped the very simple fact that no field of mathematics claims to be "correct", or that another is not. Only that no statement...
Not the end of the story. Definitions are not commutative. An axiom is indeed a "proposition regarded as self-evidently true without proof." That does...
You gave an example of a near-religious belief. It was never an axiom in a consistent mathematics.This is similar to the belief that we can't treat al...
My point is that they can't. That's why they are axioms. There are no absolute truths in Mathematics, only the concepts we choose to accept as true. W...
With all due respect, if you want "actual truth", then you do not understand the purpose of an axiom in mathematics. The point is that mathematics con...
I'm sorry, I worded that poorly. We don't establish the existence of these sets by proof. We do it by the axioms we choose to accept. And since all pr...
The problem is that CDA isn't a reductio ad absurdum proof; at least not as people think. The common presentation of it as reductio fails logically. A...
Note that this is rational number; more specifically, a rational number whose proper-form denominator is equal to (2^n)*(5*m) for integers n and m. Th...
Statistics is a branch of applied mathematics that uses probability theory to analyze, and draw inferences from, data. That's why probability theory i...
You seem to think that it is only the highest-possible v where you have an expected loss. Maybe you are confused by the fact that it was the easiest e...
No, I agree it has to be constrained to operate in the real world. That's why there has to be a real-world maximum value, you can't have an arbitraril...
It cannot be equally likely without postulating a benefactor with (A) an infinite supply of money, (B) the capability to give you an arbitrarily-small...
But it can't be unbounded and uniform. So it is inconsistent in all possible cases. What you are saying, is that if you postulate a distribution where...
Certainly. It is a complicated way of saying that, before you choose, the expected values of the two envelopes are the same. There is even a simpler w...
But it isn't logically consistent. With anything. That's what I keep trying to say over and over. 1.25v is based on the demonstrably-false assumption ...
The sample distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of si...
A normal distribution refers to a random variable whose range is (-inf,inf), and is continuous. The first cannot apply to the TEP, and the second is i...
I think this illustrates the issue you are struggling with: Say you have a perfectly-balanced cube with the numbers "1" thru "6" painted ion the sides...
I'm not sure what "real world" has to do with anything. But... Probability theory does not tell us how to define outcomes. The outcomes of a coin toss...
Exactly. Maybe I need to explain Simpson's "Paradox." It is a very similar, not-paradoxical fallacy. It just seems to be a paradox if you use probabil...
I know we are reaching an equivalent conclusion. My point is that the framework that it fits into may be different. These concepts can seem ambiguous ...
No, it isn't fair to say that. No more than saying that the probability of heads is different for a single flip of a random coin, than for the flips o...
I'll get to a more qualitative solution to the problem at the end of this post. I hope it helps. Define "interact." Say I reach into both of my pocket...
What you "cannot" do is assign probabilities to the cases. You can still - and my point is "must" - treat them as random variables, which have unknown...
I like this explanation. And I thought of a possibly better way explain how "unknown" is used in the TEP, by analogy: Say you are given a geometry pro...
The puzzling part is about our understanding the mathematics, not how we use it to solve the problem. But that still makes it a probability problem. P...
There is an interesting distribution proposed at https://en.wikipedia.org/wiki/Two_envelopes_problem#Second_mathematical_variant. Note that, like all ...
I apologize to this forum for allowing myself to be taken off topic by a troll. +++++ The difficulty with the field of probability, is that there can ...
And it is even more obvious you want to use statistics anywhere you can, no matter how inappropriate. The lexicon of both probability and statistics i...
Let's just look at our first interaction here: By this, I was clearly referring to the valid discrete sample space {"Win", "Lose"}. An event space is ...
But your expectation uses the value in the other envelope, so this is an incomplete phrasing. That's why it is wrong. And you are ignoring my comparis...
What you said was: "... uses repeated random events to make inference about an unknown distribution." Since an event is a set of possible outcomes, an...
Statistics uses repeated observations of outcomes from a defined sample space, to make inference about the probability space associated with that samp...
When all you consider is the relative chances of "low" compared to "high," this is true. When you also consider a value v, you need to use the relativ...
Why would you think that? In my opinion, the debate between Bayesian and Frequentist, or "objective" and "subjective," has nothing whatsoever to to wi...
And few have doubted it. Certainly not I - I said the equivalent many times. But that solution doesn't explain why 5v/4 is wrong, it just provides a c...
The purpose is to show why the formula (v/2)/2 + (2v)/2 = 5v/4 is wrong. The approach behind the formulation is indeed correct; it just makes a mistak...
How could anyone who has read this thread have possibly concluded that I ever made this conclusion? When all I said was that any use of statistics - w...
The *actual* truth is that you have been misinterpreting me from my very first post (), and you continue to demonstrate that here. In that post, I cit...
Described this way, the "1.25 expectation" is not fallacious, it just makes an unwarranted assumption. It is the consequences of that assumption that ...
When you deal with continuous random variables, you use the probability density function F(x). You then use events that describe ranges of values, lik...
My points have been that the results of these simulations can be proven by considering the properties of probability distributions in general, and tha...
I was being terse. A longer version of what I said is "So '2X' is meaningless if you try to use it as a value." This thread has gone on too long, and ...
And my response to these sentiments has always been that you can't define/calculate the prior distribution, and that it was a misguided effort to even...
Choosing any explicit distribution for the OP is indeed misguided, which is why your simulations were misguided. That, and the fact that your conclusi...
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