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.

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