Category:Examples of Probability Density Functions
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This category contains examples of Probability Density Function.
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be an absolutely continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $P_X$ be the probability distribution of $X$.
Let $\map \BB \R$ be the Borel $\sigma$-algebra of $\R$.
Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$.
We define the probability density function $f_X$ by:
- $\ds f_X = \frac {\d P_X} {\d \lambda}$
where $\dfrac {\d P_X} {\d \lambda}$ denotes the Radon-Nikodym derivative of $P_X$ with respect to $\lambda$.
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