Definition 7.3.1.
The uniform distribution is a continuous distribution where the probability of any interval is equal to any other interval with the same width.
The mathematical expression that describes the shape of the curve for the uniform probability distribution is called the continuous uniform probability density function:
\begin{equation*}
f(x)=\begin{cases}
\frac{1}{b-a} \amp\text{ if } a\leq x\leq b\\
0 \amp\text{ otherwise}
\end{cases}.
\end{equation*}
Since this function is a constant, the shape of the uniform probability distribution is a rectangle. So computing probabilities associated with it simply involves finding areas of rectanges:
\begin{equation*}
(\text{width})\cdot(\text{height})
\end{equation*}
