15-03-2025

Problem: Let $X$ be a continuous random variable with probability density function given by \[ f(x) = \begin{cases} ax, & 0 \leq x \leq 1 ;\\ a, & 1 \leq x \leq 2 ;\\ -ax + 3a, & 2 \leq x \leq 3 ;\\ 0, & \text{ otherwise } \\ \end{cases} \] Determine the value of $a$ and find $P(X \leq 1.5)$.