\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The random variable \(X\) has the density \(f(x) = \frac{1}{2}\), on the interval \([0, 2]\).
Find \(P(\frac{1}{2}\leq X \leq \frac{3}{4})\).
\FieldText{1}{$$\begin{aligned}[t] P\left(\frac{1}{2}\leq X \leq \frac{3}{4}\right) &=\int_{\frac{1}{2}}^{\frac{3}{4}} \frac{1}{2} \; \mathrm d x\\&=\frac{1}{2} \left[x\right]_{\frac{1}{2}}^{\frac{3}{4}}\\&= \frac{1}{2} \left[\frac{3}{4} - \frac{1}{2}\right]\\&= \frac{1}{8}\\\end{aligned}$$}