probability density function

2021-01-07 Probability shark 1 min read

Definition: A function f: $R^D \rightarrow R$ is called probability density function (pdf) if
1. $\forall x \in R^D, f(x) > 0$
2. Its integral exists and $\int_D f(x)dx = 1$

The association $P(a \leq X \leq b) = \int_b^a f(x)dx$ is called the distribution of random variable X.

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