From ddf8574ef6fb78020d00a10eea51495a17d5524f Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Fri, 28 Aug 2020 01:06:03 -0400 Subject: partially unfinished math notes --- houdre/04_foundations | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 houdre/04_foundations (limited to 'houdre') diff --git a/houdre/04_foundations b/houdre/04_foundations new file mode 100644 index 0000000..2fef43b --- /dev/null +++ b/houdre/04_foundations @@ -0,0 +1,19 @@ +HW adds problems: 9,10,14,16,17,19,20 +Will be due on Thursday or maybe two Tuesdays from now. + +A sequence is increasing if for all n >= 1, A_n \subset A_{n+1} + +P(Union of A_1..A_\infty) = \sum + +<=====> + +For increasing series lim_n->\inf P(A_n) = \sum_1^\inf P(A_i) + +For pairwise disjoint A_1..A_n, P(A_1)+...+P(A_n) = P(\union A_1..A_n) + +Conditional probability: +let A and B be two events where P(B) > 0. +P(A|B) = P(A\cap B)/P(B). + +Given, for ex., one child is a girl, the odds of the other being a girl +is 1/3 because the restricted sample space is {(G,B),(B,G),(G,G)} -- cgit