Sprinkling of a binomial random graph

Sprinkling exposes independent rounds

G (n, p_{1}), \dots, G (n, p_{k})

. Their union has distribution

G (n, p)

where

1 - p = \prod_{i = 1}^{k} (1 - p_{i}) .

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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 122 / 3 / d / Solution

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