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experiment consists of performing n independent tests

Source: Polish MO Finals 1979 p3

August 24, 2024
probabilitycombinatorics

Problem Statement

An experiment consists of performing nn independent tests. The ii-th test is successful with the probability equal to pip_i. Let rkr_k be the probability that exactly kk tests succeed. Prove that ∑i=1npi=∑k=0nkrk.\sum_{i=1}^n p_i =\sum_{k=0}^n kr_k.
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