August 2024
Beginner to intermediate
640 pages
14h 53m
Korean
Content preview from AI를 위한 필수 수학
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509
Chapter 11 -
확률
확장 정리
extension
theorem
를 사용하면 복잡한 확률 삼중항을 구성할 수 있다. 확률 측도를 거대한
시그마 대수 위에서 정의하는 대신 더 간단한 부분 집합의 집합인 반대수
semialgebra
에서 확률 측
도를 구성한다. 이후 확장 정리는 그 측도를 완전한 시그마 대수로 자동적으로 확장시킨다. 이
정리를 통해
[
0
,
1
]
구간에서의 르베그 측도
Lebesgue
measure
(이는
[
0
,
1
]
에서의 연속 균등 분포와 같
다), 곱 측도
product
measure
, 다차원 르베그 측도, 유한 및 무한 동전 던지기 등을 구성할 수 있다.
이처럼 집합 이론, 실해석학, 확률 이론의 세계는 정교하게 뒤섞여 있다.
11.8.5
확률 변수와 기대값
이제 확률 삼중항을 표본 공간과 연관시킬 수 있으므로 우리는 표본 공간의 많은 부분 집합 (연
관된 시그마 대수의 모든 원소 )에 대한 확률을 정의할 수 있다. 그리고 이를 바탕으로 엄격하
게 확률 변수를 정의할 수 있다. 엄격하지 않은 확률 이론에서도 알 수 있듯, 확률 변수는 표본
공간의 각 원소에 수치를 할당한다. 표본 공간을 어떤 실험의 가능한 모든 랜덤 결과 (
예
동전
던지기의 앞면과 뒷면 )로 생각한다면 확률 변수는 각 결과에 수치를 할당하는 것과 같다. 엄격
한 기반을 구축하기 ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.