notes

commit 5f38dd08f86c7cc54c1a1e5de0517aeb4eb746bc
parent ee5ab77051277db5d1e1bea46ba7e1f7e7a8723f
Author: Andrew <andrewlaack1@gmail.com>
Date:   Wed, 10 Jul 2024 15:32:09 -0500

Completed prob stuff

Diffstat:
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BayesTheroem.md
 | 
16
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M
ConditionalProbabilities.md
 | 
8
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A
ConditionalProbabilityTheroem.md
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14
++++++++++++++
M
StatisticsAndProbability.md
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6
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TotalProbabilityTheroem.md
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8
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5 files changed, 47 insertions(+), 5 deletions(-)
diff --git a/BayesTheroem.md b/BayesTheroem.md
@@ -0,0 +1,16 @@
+:prob: 
+# Bayes Threoem 
+
+L2
+
+## Notes
+
+**Definition:** Bayes theroem is $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
+
+This can be derived by the conditional probability theroem.
+
+Bayes theroem allows us to update the probability of some outcome given known information.
+
+## Intuition
+
+The probability that I have cancer (A) given that I have some symptoms of cancer (B) is equal to the probability that I have symptoms of cancer (B) given that I have cancer (A) multiplied by the overall probability that I have cancer (A) divided by the probability that I have symptoms (B).
diff --git a/ConditionalProbabilities.md b/ConditionalProbabilities.md
@@ -1,10 +1,10 @@
-:stats:
+:stats: :prob:
 # Conditional Probabilities
 
-Stats D2
+Stats D2 - Prob L2
 
 ## Notes
 
-**Definition:** Conditional probabilities are probabilities of something with regard to some condition.
+**Definition:** Conditional probabilities are probabilities of some outcome given some assumed condition. 
 
-An example of this is there is an 80% chance that a republican will be in favor of something. This is a conditional probability where the condition is being republican and the probability is 80%.
+An example of this is there is an 80% chance that a republican will be in favor of something. This is a conditional probability where the condition is being republican and the probability is 80%. This is in contrast with the overall probability of being republican and being in favor which also shares a sample space with republican's who aren't, liberals who are, liberals who aren't, independents who are, and independents who aren't. Given this, the overall probability is far lower than the conditional probability which is generally the case. 
diff --git a/ConditionalProbabilityTheroem.md b/ConditionalProbabilityTheroem.md
@@ -0,0 +1,14 @@
+:prob: 
+# Conditional Probability Threoem 
+
+L2
+
+## Notes
+
+**Definition:** Conditional probability theroem is $P(A|B) = \frac{P(A \cap B)}{P(B)}$.
+
+This theroem is used to find the probability of some outcome given another piece of information. This is also referred to as [[ConditionalProbabilities.md]].
+
+## Intuition
+
+The probability that A is true given B is the same as the probability of A and B divided by the overall probability of B.
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -50,4 +50,8 @@ L1:
 	- [[UniversalSet.md]]
 	- [[DisjointSet.md]]
 	- [[ProbabilityLaw.md]]
-
+L2:
+	- [[ConditionalProbabilities.md]]
+	- [[BayesTheroem.md]]
+	- [[TotalProbabilityTheroem.md]]
+	- [[ConditionalProbabilityTheroem.md]]
diff --git a/TotalProbabilityTheroem.md b/TotalProbabilityTheroem.md
@@ -0,0 +1,8 @@
+:prob: 
+# Total Probability Theroem 
+
+L2
+
+## Notes
+
+**Definition:** Total probability theroem states that the