Published
Edited
Jun 12, 2019
3 stars
md`**Product Rule:**
> ${tex.block`
\tag{2.1}
(AB|C) = F[(B|C), (A|BC)].
`}
> ${tex.block`
(AB|C) = F'[(A|C), (B|AC)].
`}
Proof by exhaustion by [Tribus, M. (1969)](https://www.amazon.com/Rational-Descriptions-Decisions-Designs-Engineering/dp/1483113817).
${tex`F(x, y)`} must be a continuous monotonic increasing function of both ${tex`x`} and ${tex`y`}:
${tex.block`
\tag{2.10a}
F_1(x, y) \equiv \frac{\partial F}{\partial x} \geq 0
`}
> ${tex.block`
\tag{2.10b}
F_2(x, y) \equiv \frac{\partial F}{\partial y} \geq 0
`}
> ${tex.block`
\tag{Associativity Equation 2.13}
F[F(x, y), z] = F[x, F(y, z)].
`}
> ${tex.block`
\tag{2.28}
w(AB|C) = w(A|BC)w(B|C) = w(B|AC)w(A|C).
`}
> ${tex.block`
\tag{2.32}
\text{Certainty is represented by } w(A|C) = 1.
`}
> ${tex.block`
\tag{Convention}
\text{Impossibility is represented by } w(A|C) = 0.
`}
`
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Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
