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The below is a picture which denotes the error of an ensemble classifier. Can someone help me understand the notation

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What does it mean to have (25 and i) in brackets and what is ε^1 is it error of first classifier or the error rate raised to power i. Can someone explain this formulae.

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    $\begingroup$ ${25 \choose i}$ is a binomial coefficient. The whole expression is the calculation of bernoulli distribution $\endgroup$
    – Nikos M.
    Commented May 22, 2022 at 9:57

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$\varepsilon^i$ is the error rate raised to the power i. So for each value i, the formula calculates the probability of i classifiers classifying a sample incorrectly, so for i=13 we have: $$e_{13\ wrong} = {25 \choose 13} \times \varepsilon^{13} \times {(1-\varepsilon)}^{12}$$ Assuming $\varepsilon = 35\%$, and calculating the binomial coefficient gives us: $$e_{13\ wrong} = 5,200,300 \times 0.35^{13} \times 0.65^{12} = 0.035$$ Repeat this for $i = 14, 15, ... , 25$, then sum all the results to get the final answer.

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