6.3 Quantile - Theory

In the video we define the lower quantile as the $LaTeX: x_{\alpha}$ $x_{\alpha}$ such that $LaTeX: P(X \leq x_{\alpha}) = \alpha$ $P(X \leq x_{\alpha}) = \alpha$ . The upper quantile is defined as the $LaTeX: x_{\alpha}$ $x_{\alpha}$ such that $LaTeX: P(X>x_{\alpha}) = \alpha$ $P(X>x_{\alpha}) = \alpha$ .

So, the lower and upper quantile are both denoted by $LaTeX: x_{\alpha}$ $x_{\alpha}$ .

To be very clear and avoid all sources of confusion, we can denote the lower quantile by: $LaTeX: x_{\alpha} ^{lower}$ $x_{\alpha} ^{lower}$ and the upper quantile by: $LaTeX: x_{\alpha}^{upper}$ $x_{\alpha}^{upper}$ if we wish.

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