50008: Cleanup of section levels

Author: OliverKillane

50008 - Probability and Statistics/50008 - Probability and Statistics.pdf

@@ -1,6 +1,6 @@
 \chapter{Joint Random Distributions}
 
-\subsection{CDF}
+\section{CDF}
 Suppose we have random variables $X$ and $Y$ such that:
 \[X: S_X \to \mathbb{R} \ \text{ and } \ Y: S_Y \to \mathbb{R}\]
 We can define $Z$ operating on sample space $S$ such that:
@@ -29,7 +29,7 @@ \subsection{CDF}
 Hence we can get the interval:
 \[P_Z(x_1 < X \leq x_2, y_1 < Y \leq y_2) = F(x_2, y_2) - F(x_1, y_2) -F(x_2,y_1) + F(x_1,y_1)\]
 
-\subsection{PMF}
+\section{PMF}
 \begin{definitionbox}{Joint Probability Mass Function}
 	\[p(x,y) = P_Z(X = x, Y = y) \ \text{where } x,y \in \mathbb{R}\]
 	We can get the original \keyword{pmfs} of the two variables as:
@@ -41,7 +41,7 @@ \subsection{PMF}
 	\end{itemize}
 \end{definitionbox}
 
-\subsection{PDF}
+\section{PDF}
 \begin{sidenotebox}{Fundamental Theorem of Caculus}
 	The fundamental law that integration and differentiation and the inverse of each other (except for constant added in integration $c$, which does not affect definite integrals).
 \end{sidenotebox}

50008 - Probability and Statistics/joint_random_distributions/joint_random_distributions.tex

@@ -145,7 +145,7 @@ \subsection{Bernoulli Distribution}
 		\end{split}\]
 \end{sidenotebox}
 
-\subsection{Normal Distribution - Single DataPoint Sample}
+\subsection{Normal Distribution - Single Datapoint Sample}
 Given some $x|\mu \thicksim N(\mu, \sigma^2)$ where $\sigma^2$ is known and $\mu$ is unknown. Using a sample of a single datapoint $x$.
 \\
 \\ \textbf{Step 1.} The likelihood can be found using the \keyword{Normal Distribution PDF}: