3.5 What quality does the probability density function have ?

Let $\pi$ be a continuous random variable with probability density function $f(\pi)$. Then $f(\pi)$ has the following properties:

• The proportion has to be greater than or equal to zero

$$f(\pi) \geq 0$$

• The area under the curve sums to 1

$$\int_{\pi} \! f(\pi) \, d\pi = 1$$

• The area under the curve between a and b sums to the probability of pie being in that range.

$$P(a < \pi < b) = \int_{a}^{b} \! f(\pi) \, d\pi$$