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Scientific Computing & Data Science

[Probability] Normal Distribution - Averaging Independent Normal Random Variables 본문

Data Science/Probability & Statistics

[Probability] Normal Distribution - Averaging Independent Normal Random Variables

cinema4dr12 2014. 2. 21. 22:41

만약 확률변수 Xi ~ N(μ,σ2), 1 ≤ i ≤ n 가 독립 확률 변수라면 이들의 평균

는 다음의 분산을 따른다:


[Proof]

이므로

이며,

이므로

따라서,

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