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Equation 14 · Part 4 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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