>>6832 (OP)
Уебывай. Домашку тут не делают! Тут серьезные люди, серьезно обсуждают бредовые околонаучные маняфантазии залетных школьников из /b
обратись в /math
но учитывай, что с вероятностью 4/5 там тебя тоже пошлют нахуй

>>6833
Thanks for the reply (I hope you can understand English)
This isn't homework. I've posted this question on English math forums an d no one has been able to come up with an answer.

Since the problem originates from a Russian book, I thought it'd appropriate to ask here for help.

>>6832 (OP)
Попробуй напрямую решить: выписываешь выражение вероятнисти в интегральной форме (интеграл с дельтой), для искомой случайной величины считаешь индикатриссу, методом перевала находишь асимптотику интеграла и считаешь обратный фурье-образ.

>>6836
будь честнным с собой ты матиматик или вычеслиьедб

>>6834
Assuming this is not pasta/trolling

Hey mate, I think you can use the following properties to solve this
- distribution of a sum of r. v. is their convolution
- inverse fourier transform of a convolution is just the product of inverse fourier transforms
Use induction if you struggle to keep all indices in check

As mentioned above, /math/ is a much better suited board for this, /sci/ is basically just brainlets regurgitating popsci bullshit about ether and quantum mechanics

You can also try and check out some of the published statistical papers that propose new tests - they often calculate the resulting distributiondistribution as a asymptotic for a combination of known distributions like gamma and shit

>>6860
thanks for your answer

The distribution of X+Y is the convolution of the distribution only when X and Y are independent

The major hurdle in this problem is that the variables in the sum are correlated, so one can't use convolutions or characteristic functions.

Do you know active Russian math forums where I could get an answer ? The problem book by Shiryaev is fairly well-known, and it seems that it's used in courses at MSU. So there's a chance this exercise has already been discussed somewhere...

>>6865

>Do you know active Russian math forums where I could get an answer ?

dxdy.ru
also try math.stackexchange

>>6869
I've already tried both

No match on dxdy

The question has been asked in 2014 on math.stackexchange, no answer since then...

>>6870

>No match on dxdy

I meant, ask there, it's the top math forum in ru web
it's super strict rules-wise though, so you have to use googel translate and present your own attempt at solution if you want to get any help
If I have time this weekend I will ask there myself and will translate you all the comments

>>6832 (OP)
Чувак, ты на название параграфа смотрел? § 4. Центральная предельная теорема для сумм независимых случайных величин. I. Условие Линдеберга
https://ru.wikipedia.org/wiki/Центральная_предельная_теорема
Чего тебе ещё надо чтобы решить?

>>6832 (OP)
Могу набросать тебе решение. Нужно?

>>7715
Да, набросай. Интересно