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Statistics and Probability/Mock exam run 1.md

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+
+### Null hyposthesis
+
+### Confidence interval
+Interval which is expected to contain the parameter
+$$
+CI = \bar{x} \pm z \frac{s}{\sqrt{n}}
+$$
+Where $z\frac{s}{\sqrt{n}}$ is the variation in our estimate.
+
+
+### T-Test
+Used to determine if there is a significant difference between the means of two groups.
+
+We have to assume:
+- Data follows a normal distribution
+- each observation is independent
+
+$$
+t = \frac{\text{mean} - \text{theoretical value}}{s\sqrt{n}}
+$$

Statistics and Probability/Support Lecture.md

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