Interval and conditional probabilities from a density
Let X be a continuous random variable with probability density function f
\[f(x)=\frac{3}{8}\,x^{2}\quad(0\le x\le 2)\]
\[f(x)=0\quad\text{outside }[0,2]\]
The event is \(\frac{1}{2}<X<\frac{5}{4}\)