notes

commit 6a64183b162c0dc130a3ecd9f85d104060f821af
parent c0960c2427527e84db8db5a0224ca9a84428865c
Author: Andrew <andrewlaack1@gmail.com>
Date:   Fri, 31 May 2024 14:37:56 -0500

Added notes for stats

Diffstat:
A
ContinuousProbability.md
 | 
12
++++++++++++
A
DiscreteProbability.md
 | 
8
++++++++
M
Probability.md
 | 
2
+-
A
ProbabilityDensityFunctions.md
 | 
10
++++++++++

4 files changed, 31 insertions(+), 1 deletion(-)
diff --git a/ContinuousProbability.md b/ContinuousProbability.md
@@ -0,0 +1,12 @@
+:stats:
+# Continuous Probability
+
+Stats Ch1
+
+## Notes
+
+**Definition:** A continuous probability is one where there are an uncountable number of outcomes. 
+
+This is often defined by intervals either finite or infinite.
+
+To graph continuous probabilities we often use density (kde) graphs to show probability of any given input lasting an amount of time. These are referred to as [[ProbabilityDensityFunctions.md]] of pdfs. While histograms fill a similar role, they are not considered a pdf because they use bins instead of continuity.
diff --git a/DiscreteProbability.md b/DiscreteProbability.md
@@ -0,0 +1,8 @@
+:stats:
+# Discrete Probability
+
+Stats ch1
+
+## Notes
+
+**Definition:** A discrete probability is one where there are a finite set of outcomes or a countably infinite set of outcomes.
diff --git a/Probability.md b/Probability.md
@@ -11,7 +11,7 @@ Let X be a set and F a set of subsets of X. A probability on (X,F) is a function
 
 The probability function must be a set function, but that is not sufficient. We also need for u(0) where 0 is the empty set to be equal to 0. We also need u(X) = 1 (totaling 100%), and if A and B are disjoint sets then u(A union B) = u(A) + u(B). This final part means the probability of the union of two different sets is equal to the sum of the probabilities of both sets individually. 
 
-When we have a domain that is finite we then state we have a discrete probability whereas when we have an interval then the function is said to be a continuous probability.
+When we have a domain that is finite we then state we have a [[DiscreteProbability.md]] whereas when we have an interval then the function is said to be a [[ContinuousProbability.md]].
 
 In practical terms, for u(X) X is the set off outcomes that are possible and the function returns the probability of said outcome. 
 
diff --git a/ProbabilityDensityFunctions.md b/ProbabilityDensityFunctions.md
@@ -0,0 +1,10 @@
+:stats:
+# Probability Density Functions (PDFs)
+
+Stats ch1
+
+## Notes
+
+**Definition:** A probability density function shows the probability of outcomes for [[ContinuousProbability.md]] problems.
+
+Think of KDEs and kind of histograms. The difference with histograms is they use bins instead of a continuous probability graph.