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Equation 14 · Part 10 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

Ending index or upper bound: n

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

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

n occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

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Sources cited in the article section

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