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@jemoka / Jemoka Knowledge Base / raw/concept/kbhrelative_probability.md
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--- title: "relative probability" source: https://www.jemoka.com/posts/kbhrelative_probability/ --- Let \(X \sim \mathcal{N}\). “How much more likely is \(x=10\) than \(x=5\)?” We note that \(P(x=value) = 0\) for any value if \(X\) is continuous. However, we can still get an answer: \begin{equation} \frac{\dd{X} P(x=10)}{\dd{X} P(x=5)} \end{equation} these two things cancel out. Therefore, you can just divide the PDF: \begin{equation} \frac{f(x=10)}{f(x=5)} \end{equation}