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Equation 7 · Part 4 · Measuring AI Agent Reliability: What the Evidence Actually Supports

Symbol c

pass@k  :=  Etasks ⁣[ 1  −  (n−ck)(nk) ]\text{pass@}k \;:=\; \mathbb{E}_{\text{tasks}}\!\left[\, 1 \;-\; \frac{\binom{n-c}{k}}{\binom{n}{k}} \,\right]
cc

What this part means

c occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

c occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…estimate but a high-variance one, since it throws away information every time you happen to generate more or fewer than k samples. Their fix was to over-sample: draw n total samples per task, observe how many of them, c , actually pass, and then compute the exact probability that a random draw of k items from those n would contain at least one success [ 2 ] . That combinatorial form is the unbiased estimator: it uses every one of the n observed outcomes rather than discarding some of them, and it has materially…

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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 surrounding passage

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