vault backup: 2025-01-13 15:32:46

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
+$$
+var(X) = \mathbb{E}[X^2] - (\mathbb{E}[X])^2
+$$
+
+##