commit 90a479bdf99f27ff911ce9e0e8d3fb0e3661dd38
parent 90e19bfd85e880fa4f21f37751177b524bb7287f
Author: Andrew <andrewlaack1@gmail.com>
Date: Tue, 27 Aug 2024 15:50:34 -0500
Added yesterdays notes for stats
Diffstat:
5 files changed, 44 insertions(+), 5 deletions(-)
diff --git a/BinomialCoefficient.md b/BinomialCoefficient.md
@@ -1,4 +1,4 @@
-:prob:
+:prob: :stats:
# Binomial Coefficient
L4
@@ -26,3 +26,7 @@ The top of the function is all permutations of the list. The problem with this i
As such, we divide this by r! to account for the arrangements of the r items. The second part, (n-r!) accounts for arrangements where we are not choosing r items.
All together, we find the permutations of sets length n then divide this by r! to find the number of distinct sets not arrangements and then we divide by (n-r)! to get rid of sets that don't have r items.
+
+### Stats
+
+In stats we often denote this using either the vertical denotation or the denotation $_nC_r$ where n is the length of the set and r is the size of each subset.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -90,3 +90,17 @@ Unit 2.4 (integers and division):
- [NumberTheory](NumberTheory.md)
- [CompositeNumber](CompositeNumber.md)
- [PrimeNumber](PrimeNumber.md)
+ - Mersenne Prime
+ - div (function)
+ - mod (function always greater than 0 including for negatives)
+ - relatively prime (gcd)
+ - pairwise relatively prime
+ - prime factorization (describe how to find with prime exponent calculation)
+ - gcd (describe prime factorization use to find it)
+ - lcm (describe again how to find with prime factorization)
+ - ab = gcd(a,b) x lcm(a,b)
+ - congruence (a \equiv b (mod c))
+ - congruence class
+ - pseudo random number generation (linear congruential model and pure multiplicative gen)
+ - caesar cipher
+ - vigenere cipher (polyalphabetic ciphers)
diff --git a/OrderedSample.md b/OrderedSample.md
@@ -0,0 +1,8 @@
+:stats: :prob:
+# Ordered Sample
+
+CH 1.3
+
+## Notes
+
+**Definition:** An ordered sample is an outcome where the order of elements contributes to the uniqueness of the output. As such, an ordered sample is denoted using ordered pairs instead of a set as sets are innately unordered.
diff --git a/Permutation.md b/Permutation.md
@@ -0,0 +1,14 @@
+:stats:
+# Permutation
+
+CH 1.3
+
+## Notes
+
+**Definition:** A permutation is an arrangement of elements length n.
+
+To calculate the total number of permutations of a given list we simply find the length, denoted n, factorial.
+
+In stats there is also a denotation $_nP_r$ which is the number of permutations of the set length n where each permutation is of length r. This is similar to the binomial coefficient except the binomial coefficient describes subsets and thus there is no order making the number of subsets = $\frac{_nP_r}{r!}$.
+
+$_nP_r = \frac{n!}{(n-r)!}$
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -26,10 +26,9 @@ Chapter 1.2:
- [[SetFunction.md]]
Chapter 1.3:
- - Permutation (denote \_nP\_r permutations of n objects taken r at a time)
- - When discussing subset based permutations we need bare in mind that binomial coefficients are discussing true subsets whereas permultations of the form nPr are descrbing permultations of r length of a set n long thus they are not ordered and thus are r! higher in count than the binomial coefficient (useful for deriving binomial coefficient formula).
- - Binomial Coefficient (denote \_nC\_r )
- - Ordered sample
+ - [Permutation](Permutation.md)
+ - [BinomialCoefficient](BinomialCoefficient.md)
+ - [OrderedSample](OrderedSample.md)
---
