diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 5c07728..27c45f5 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -27,12 +27,12 @@ "state": { "type": "markdown", "state": { - "file": "Extracurricular/Misc/Ideas.md", + "file": "Statistics and Probability/Support Lecture.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Ideas" + "title": "Support Lecture" } } ], @@ -92,7 +92,8 @@ } ], "direction": "horizontal", - "width": 234.5 + "width": 234.5, + "collapsed": true }, "right": { "id": "fd4347e6b5300816", @@ -215,9 +216,10 @@ }, "active": "3dbe2cc922c4bee2", "lastOpenFiles": [ + "Pasted image 20250113151159.png", + "Extracurricular/Misc/Ideas.md", + "Statistics and Probability/Support Lecture.md", "Functional Programming/Drawing 2024-12-24 17.52.22.excalidraw.md", - "Extracurricular/Misc/Ideas.md", - "Extracurricular/Misc/Ideas.md", "Extracurricular/satQuest/Meeting Dec 18.md", "Extracurricular/satQuest/img/Pasted image 20241218122110.png", "Excalidraw/Drawing 2024-12-11 23.27.51.excalidraw.md", @@ -250,7 +252,6 @@ "Advanced Programming/Intro.md", "Advanced Programming/Annotation Repository.md", "Advanced Programming/projects/API Design Research.md", - "Advanced Programming/projects/first/Specification.md", "Advanced Algorithms/assets/pnp/Pasted image 20241203234013.png", "Advanced Algorithms/assets/pnp/Pasted image 20241203234032.png", "Advanced Algorithms/assets/graph/1_WR4AtjT_nhwSOtAW99Yd5g.gif", diff --git a/Pasted image 20250113151159.png b/Pasted image 20250113151159.png new file mode 100644 index 0000000..8e36d28 Binary files /dev/null and b/Pasted image 20250113151159.png differ diff --git a/Statistics and Probability/Support Lecture.md b/Statistics and Probability/Support Lecture.md new file mode 100644 index 0000000..a0d0c9c --- /dev/null +++ b/Statistics and Probability/Support Lecture.md @@ -0,0 +1,42 @@ +## Probability +- $P = \frac{\text{Favorable Cases}}{\text{Total Cases}}$ + +### Conditional Probability + +$$ +P (A|B) = \frac{P (A \cap B)}{P(B)} +$$ + + +### Independence +$$P (A \cup B) = P(A)P(B)$$ + +### Law of Total Probabilities + +Used when selecting an element at random. + +$$ +P(A) = \Sigma_n P(A \cup B_n) +$$ + +![](Pasted%20image%2020250113151159.png) +### Bayes' theorem + +$$ + P(H | \epsilon) = \frac{P(\epsilon | H) P(H)}{P(\epsilon)} +$$ + + +### Probability Mass Function (PMF) +- Helps more finding the mean than the variance + + +### Expectation ($\mathbb{E}$) +idfk +**Expected value == mean** +### Variance +$$ +var(X) = \mathbb{E}[X^2] - (\mathbb{E}[X])^2 +$$ + +## \ No newline at end of file