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Equation 14 · Part 7 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

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p^=1n∑i=1n1[trial i succeeded],\hat{p} = \frac{1}{n}\sum_{i=1}^{n} \mathbb{1}[\text{trial } i \text{ succeeded}],
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Write the naive estimate over n independent trials as p^=1n∑i=1n1[trial i succeeded]\hat{p} = \frac{1}{n}\sum_{i=1}^{n} \mathbb{1}[\text{trial } i \text{ succeeded}]. and contrast it with a severity-weighted version,

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.