здравствуйте уважаемое сообщество
учусь на втором курсе прикладной математики Каунасского Технологического Университета.
проблема такая - делаем презентацию на английском языке по предметной области математики на 6 минут со сладами.
я решил сделать по случайным числам и генератору случайных чисел отсюда
https://en.wikipedia.org/wiki/Randomnessи отсюда
https://en.wikipedia.org/wiki/Pseudorandom_number_generatorПомогите пожалуйста как озвучить формулы и математические выражения на английском языке
читать дальше
==Mathematical definition==
Given
`mathfrak(B, C, I, H, R, Z)`
* `P` - a probability distribution on `( \mathbb(R), mathfrak(H) )` (where `mathfrak{H}` is the standard Borel field on the real line)
* `\mathfrak{C}` - a non-empty collection of Borel sets `\mathfrak{C}\subseteq\mathfrak{H}`, e.g. `\mathfrak{C}= \{ (-\infty,t\ ] : t\in\mathbb{R} }`. If `\mathfrak{C}` is not specified, it may be either `\mathfrak{H}` or `{ (-\infty,t] : t\in\mathbb{R}\}`, depending on context.
* `A\subseteq\mathbb{R}` - a non-empty set (not necessarily a Borel set). Often `A` is a set between `P` 's Support (mathematics)|support]] and its [[Interior (topology)|interior]], for instance, if `P` is the uniform distribution on the interval `(0,1]`, `A` might be `(0,1]`. If `A` is not specified, it is assumed to be some set contained in the support of `P` and containing its interior, depending on context.
We call a function `f:\mathbb{N}_1\rightarrow\mathbb{R}` (where `\mathbb{N}_1={1,2,3,\dots }` is the set of positive integers) a '''pseudo-random number generator for `P` given `\mathfrak{C}` taking values in `A` ''' iff
* `f (\mathbb{N}_1 )\subseteq A`
* `\forall E\in\mathfrak{C} \quad \forall 0<\varepsilon\in\mathbb{R} \quad \exists N\in\mathbb{N}_1 \quad \forall N\leq n\in\mathbb{N}_1, \quad |\frac{\# {i\in {1,2,\dots, n } : f(i)\in E }}{n}-P(E) |< \varepsilon`
(`#S`> denotes the number of elements in the finite set `S`.)
It can be shown that if `f` is a pseudo-random number generator for the uniform distribution on `(0,1)` and if `F` is the [[Cumulative distribution function|CDF]] of some given probability distribution `P`, then `F^*\circ f` is a pseudo-random number generator for `P`, where `F^*: (0,1)\rightarrow\mathbb{R}` is the percentile of `P`, i.e. `F^*(x):=\inf {t\in\mathbb{R} : x\leq F(t) }`. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard uniform distribution.
простите пожалуйста, если не совсем по теме
thanks in advance