From 63cc4016987401db3ee023e580d0b90ffb77db87 Mon Sep 17 00:00:00 2001 From: eggy Date: Fri, 31 Mar 2023 11:50:17 -0400 Subject: [PATCH] ece108: add bayes law 2 --- docs/1b/ece106.md | 2 ++ docs/1b/ece108.md | 5 +++++ 2 files changed, 7 insertions(+) diff --git a/docs/1b/ece106.md b/docs/1b/ece106.md index d2d0463..92bbd01 100644 --- a/docs/1b/ece106.md +++ b/docs/1b/ece106.md @@ -666,3 +666,5 @@ If there is a conducting loop in a time-varying magnetic field, a $V_{ind}$ is f $$V_{ind}=\oint\vec E\bullet\vec{d\ell}=-\frac{d}{dt}\int\vec B\bullet\vec{dS}$$ Time-varying magnetic fields are formed if the field or charge is moving or if bounds change. + + diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md index 868a5f3..76467e2 100644 --- a/docs/1b/ece108.md +++ b/docs/1b/ece108.md @@ -927,3 +927,8 @@ $$\text{independent}\iff Pr\{A\cup B\}=Pr\{A\}+Pr\{B\}-Pr\{A\}Pr\{B\}$$ **Bayes' theorem** provides a general formula for conditional probability: $$Pr\{A|B\}=\frac{Pr\{B|A\}}{Pr\{B\}}$$ + +Formally, this can be solved without $Pr\{B\}$: + +$$Pr\{A|B\}=\frac{Pr\{A\}Pr\{B|A\}}{Pr\{A\}Pr\{B|A\}+Pr\{\overline A\}Pr\{B|\overline A\}}$$ +