← Back to article

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

What does this equation mean?

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

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Start with1
Divide byn
This relates tohatp
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

p^\hat{p}

Symbol hatp

the naive estimate over n independent trials.

Understand this part →

nn

Symbol n

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

Understand this part →

ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Understand this part →

=

=

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

Understand this part →

See an illustrated explanation →
fraction

fraction

Divide the expression above the line by the one below it.

Understand this part →

See an illustrated explanation →
subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

superscript

superscript

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.

Understand this part →

See an illustrated explanation →
11

Numerator: 1

The complete quantity above the fraction bar.

Understand this part →

i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Understand this part →

nn

Ending index or upper bound: n

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

Understand this part →

How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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,

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

See this formula across 1 published context →

Browse the mathematical compendium →