\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the function \(f(x) = a\).
Find the value of \(a\) such that \(f(x)\) is a probability density function on the interval \([0, 2]\).
\FieldText{1}{$$\begin{aligned}[t] 1&= \int_{0}^{2} a \, dx \\1&= a \left[ x \right]_{0}^{2} \\1&= a \left( 2 - 0 \right) \\1&= 2a \\a &= \frac{1}{2}\end{aligned}$$}