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defence/pearson-corr-sample.tex

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+\documentclass[convert={density=500}, border=2pt, varwidth=3in]{standalone}
+
+\usepackage{amsmath}
+\usepackage{amssymb}
+
+\begin{document}
+
+\begin{align*}
+r_{X, Y} &= \frac{
+\sum_{i=1}^n(x_i - \overline{x})(y_i - \overline{y})
+}{
+\sqrt{
+\sum_{i=1}^n(x_i-\overline{x})^2
+}
+\sqrt{
+\sum_{i=1}^n(y_i-\overline{y})^2
+}
+}
+\end{align*}
+
+\end{document}

defence/pearson-corr.tex

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+\documentclass[convert={density=500}, border=2pt, varwidth=2in]{standalone}
+
+\usepackage{amsmath}
+\usepackage{amssymb}
+
+\begin{document}
+
+\begin{align*}
+\rho_{X,Y} &= \frac{\mathrm{cov}\left(X, Y\right)}{\sigma_X \sigma_Y}
+\end{align*}
+
+\end{document}