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Equation 10 · Part 13 · How Fast Can a Horizon Learn Which Path You Took?

Denominator: 2

pe(T)=1−D(T)2=1−1−V(T)22.p_{\rm e}(T)=\frac{1-D(T)}{2} =\frac{1-\sqrt{1-V(T)^2}}{2}.
22

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

2 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Helstrom’s binary decision theory supplies the minimum average probability of guessing the wrong path: pe(T)=1−D(T)2=1−1−V(T)22p_{\rm e}(T)=\frac{1-D(T)}{2} =\frac{1-\sqrt{1-V(T)^2}}{2}. For the balanced pure-state problem, the minimum-error measurement induces a symmetric binary channel. Its recovered decision information is

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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