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Maths Facts

@mathsfacts.bsky.social
5 followers 8 following 2 posts

Sharing random interesting maths facts. By @maxal.bsky.social

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Maths Facts @mathsfacts.bsky.social · 14/12/2024
The bootstrap can be used to generate a new random sample from an existing random sample. Its validity can be guaranteed by the Glivenko-Cantelli theorem, which demonstrates how the empirical cumulative distribution (CDF, top panel), converges on the CDF of the sample (bottom panel).
The bootstrap can be used to generate a new random sample from an existing random sample. It's validity can be guaranteed by the Glivenko-Cantelli theorem, which demonstrates how the empirical CDF (top panel), converges on the CDF of the sample (bottom panel).
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Maths Facts @mathsfacts.bsky.social · 14/12/2024
For an increasing function 𝑓:ℝ→ℝ, max(𝑓(𝑎),𝑓(𝑏))=𝑓(max(𝑎,𝑏)). An important special case is 𝑓(𝑥)=𝑥+𝑐, for which we obtain max(𝑎+𝑐,𝑏+𝑐)=𝑐+max(𝑎,𝑏).
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