It's not really a problem, but I wonder how to express an expression (sorry for such a poor language) inside pdf system as a function of another? For example we have pdf is $$\begin{cases} a&0\le x\le0.5\\ b&0.5<x\le1\\ 0&\text{otherwise} \end{cases}$$ Is there any chance to express $b$ in terms of $a$?
2026-04-03 02:19:26.1775182766
How to express probabilities as a function of another inside pdf?
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Assuming $0 \leq x \leq 1$ and $f(x)$ is your pdf, you can write this:
$$1 = \int_0^1 f(x)\,dx = \int_0^{0.5} a\,dx + \int_{0.5}^1 b\,dx = 0.5a + 0.5b \implies b = 2 -a$$