n be the area of the largest disk that can be drawn in [0, 1]² which es not contain any point {P₁, P2, ..., Pn}. Show that nMn → ∞ P n→∞

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12. Let (Pn) be iid points on [0, 1]² whose law has some density f. Let
Mn be the area of the largest disk that can be drawn in [0, 1]2 which
does not contain any point {P₁, P2,..., Pn}. Show that nMn
P
1
(meaning that nmn
Mn
P
n→00²
→ 0).
n→∞
Transcribed Image Text:12. Let (Pn) be iid points on [0, 1]² whose law has some density f. Let Mn be the area of the largest disk that can be drawn in [0, 1]2 which does not contain any point {P₁, P2,..., Pn}. Show that nMn P 1 (meaning that nmn Mn P n→00² → 0). n→∞
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