Equation 9 · Part 3 · Building a Production-Grade MCP Server
Symbol p
What this part means
the some true success probability.
Its job in the formula
p occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Symbol p→Article meaning
Where the article explains it
A model’s behaviour on a given prompt is not deterministic across runs, so a single trial is one draw from a Bernoulli process with some true success probability p , and the uncertainty in an observed rate from n independent trials shrinks only as .
The passage around this formula
. To bound that uncertainty to a half-width e at a chosen confidence level z , the standard requirement is . which, for a rate near one half and a 95% confidence interval within five percentage points, already calls for several hundred independent trials rather than five or ten. The practical conclusion is not that every team needs a statistics department before shipping a tool; it is that “it passed when I tried it a few times” and “it passes at a known, bounded rate” are different claims, and only a CI-integrated harness run at real scale can make the second one.
Learn the underlying idea
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Open the illustrated functions: inputs become outputs guide →
See this notation across published equations →
Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.