# Probability Density Function

Used in the context of continuous Random Variable. See PMF for discrete random variables.

In Probability, a PDF is a function whose value at any given point in the sample space can be interpreted as the relative likelihood that the value of the random variable would be equal to that sample.

These functions help model out the distribution of a particular variable, such as the age at which humans die, the height of a population, or suppose bacteria of a certain species typically live 4 to 6 hours. Then you can create a PDF.

for example, Normal Distribution has probability density $f(x)=2π 1 e_{−x_{2}/2}$

PDF to CDF

- $F(x)=∫_{−∞}f(y)dy$

For a PDF $f(x)$, we need to satisfy the condition $∫f(x)dx=1$ This is why it is possible for $f(x)$ to be $>1$, if on the x-axis the interval is $<1$, for example on interval $[0,21 ]$

### Related

- See Distribution for conversions
- Probability Mass Function