Probability Density Function

A Probability Density Function is a Probability Function for a Continuous Distribution, that is, where the Random Variable is Continuous. It is called a density function, because each probability value doesn’t have a value at its exact Outcome, just zero, rather, only continuous ranges of outcomes produce a probability. Just like how a single point in a solid doesn’t have a mass, only over a region with a density is there a mass.

• $|S|>{\aleph }_0$
• $\forall x\in S,f(x)\ge 0$
• $\forall x\in \mathbb{R},P(X=x)=0$
• ${\int }_{-\infty }^{\infty }f(x)dx=1$
• $P(a\le X\le b)={\int }_a^{b}f(x)dx=F(b)-F(a)$