Recent content by la6ki

Hi guys and thank you for your replies. I think my worries of not being able to ask my question properly are somewhat confirmed. I'll try to ask 2 additional questions that may serve a better role: 1. Are there any physical theories which (ultimately) rely on mathematical axioms? For instance...

I am not a mathematician but, as such, I think I have a pretty good background in mathematics. I have a good understanding and experience with calculus, differential equations, linear algebra, and probability theory. I also have interest in abstract algebra concepts, though I wouldn't say I am...

As I suspected, I was definitely making it more complicated for myself :) Thanks for the help guys, I managed to solve it. I'm still not too experienced and sometimes obvious things don't immediately hit me in the face.

I've been trying to work on differential equations using several books and one of the first exercise questions I encountered already has me stuck. The momentum p of an electron at speed v near the speed c of light increases according to the formula p=mv/√(1-v^2/c^2), where m is a constant...

I certainly agree, but that happens according to the result. Meaning, depending on what the result actually is, we can increase, decrease, or not change our probability. But this isn't the case with the CI problem. Regardless of what the interval actually is, we cannot say that it has a...

But once I've seen the interval, I still don't know what the mean is, so the analogy isn't exactly correct. In my opinion the coin example I gave exactly captures the CI situation. Before I tossed a coin, what is the probability that it will come up heads? It's 0.5 After I toss it, but before I...

The thing is that, I actually tried making a philosophical point about the statistical method itself. Clearly, it is irrational NOT to consider the second interval as much more likely than the other 2. But if the theory underlying frequentist statistics says otherwise, there must be something...

Thank you for the links! I was actually curious if there was a discussion like this from the perspective of physics, so it sounds like a really interesting read. Do physicists ever use p-values and the like? Clearly, the most important theories were developed without any reference to them...

But I'm a little suspicious that even that minority would be able to resist the temptation. In any case, they would secretly know that if they choose the second interval, they can be all but sure they will leave with $50 000 in their pocket, whereas if they choose any of the other intervals...

Thank you all for the replies. I don't understand the difference between before I looked at the result and after I looked at it. Since looking at it doesn't actually change anything (it's a passive process), why should the probability collapse from 95% to 0 or 1? Do I understand correctly...

Hi all. I've been thinking about this question a lot for the past few days and it seems to me that I'm committing a mistake somewhere along the way, but certainly can't figure out where. Here's one of the interpretations which I've encountered most frequently and think is the right one (here's...

Thanks a lot for all the recommendation, guys! Well, now I realize that the word "decent" can mean very different things for a mathematician and for a non-mathematician :) I guess what I actually meant was that I have the rough basics of probability theory (like having some experience with...

Well, I don't only have specific end goals in mind and I would like to have a deep theoretical understanding of the field as well. So, one of the end goals would be, as I said, to reach the level at which I can understand the book I cited from. Otherwise, stochastic differential equations...

Thank you for your detailed response. I must say that I already have a decent background in probability theory, so I don't know how much I should work on it before I move on. Would you actually recommend to read a book on measure theory as a next step, or try to find a book on probability...

I wouldn't say I study those things as a hobby. I am studying neuroscience and want to have a very solid background in physics and decided that in order to achieve that, I will also need a very solid background in math. Also, advanced probability theory that I'm also trying to learn (this is an...