Formal Definition
(This definition may be extended to any probability distribution using the measure-theoretic definition of probability.)
A random variable X with values in a measure space (usually Rn with the Borel sets as measurable subsets) has as probability distribution the measure X∗P on : the density of X with respect to a reference measure μ on is the Radon–Nikodym derivative:
That is, f is any measurable function with the property that:
for any measurable set .
Read more about this topic: Probability Density Function
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