We model a realistic event of everyday life with a continuos probability density function.
What information about the probabilities of the event is carried by the fact that the probability density function is a continuos function ?
2026-04-07 11:09:53.1775560193
Continuity of probability density function
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That the cumulative distribution function $P(X\le X)$ is absolutely continuous with respect to the Lebesgue measure (the Cantor distribution shows the CDF's continuity is insufficient for a continuous distribution).