Probability density function

The probability density function of a continuous random variable is a function that describes the probability of the variable taking on a value lower than x.

It’s just a normal function so we write it as f(x) (or another letter than f).

Conditions

If f(x) is a valid density function, then it needs to be true that:

• f(x)\geq 0 (it can’t ever give a negative probability)
• \int_{-\infty}^\infty f(x)\,dx=1 (probabilities add up to one)