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probability density function

We call X a continuous random variable if X can take any value on an interval, which is often the entire set of real numbers R.

Every continuous random variable X has a probability density function (PDF), written f(x), that satisfies the following conditions:

  1. \forall x \in \mathbb{R}^D: f(x) \geq 0
  2. \int_{\mathbb{R}^D}f(x)dx = 1
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