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Equation 14 · Part 1 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

Symbol hatp

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

What this part means

the naive estimate over n independent trials.

Its job in the formula

hatp is part of the quantity the equation computes from the expression on the right.

Where the article explains it

Write the naive estimate over n independent trials as p^\hat{p} = 1n\frac{1}{n}∑i=1n\sum_{i=1}^{n} 1\mathbb{1}[trial \text{trial } i  succeeded\text{ succeeded}], and contrast it with a severity-weighted version, R = 1 - ∑i=1n\sum_{i=1}^{n} wiw_i ⋅\cdot 1\mathbb{1}[trial \text{trial } i  failed\text{ failed}], where wiw_i scales each failure by how costly it actually was.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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