Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

Independent-trial statistical certificate

Destructive verification and complete records › Independent-trial statistical certificate · lines 1705–1721

Suppose $n_{x}, n_{x^{'}}$ independent attempted trials are made with fixed preparations and fresh independent apparatus. For $0 < β < 1$ , set

u_{x} = \frac{lo g ( 4/ β )}{2 n _{x}}, u_{x^{'}} = \frac{lo g ( 4/ β )}{2 n _{x^{'}}} .

Then with probability at least $1 - β$ ,

∣ p_{x} - p_{x^{'}} ∣ \geq Δ - e_{x} - e_{x^{'}} - u_{x} - u_{x^{'}},

where $Δ$ is the named ideal event gap.

Displayed formulas in this passage

unlabeled · line 1710
$u_{x} = \frac{lo g ( 4/ β )}{2 n _{x}}, u_{x^{'}} = \frac{lo g ( 4/ β )}{2 n _{x^{'}}} .$
unlabeled · line 1715
$∣ p_{x} - p_{x^{'}} ∣ \geq Δ - e_{x} - e_{x^{'}} - u_{x} - u_{x^{'}},$