Question : A random variable X has a pdf

f(x) = $\displaystyle \begin{cases}

Ax , & \mbox{0 } \le \mbox{ x} < \mbox{ 5} \\

A(10 -x) , & \mbox{5} \le \mbox{ x} < \mbox{10} \\

0, & \mbox{otherwise }

\end{cases}$

i) Determine $\displaystyle A$

ii) Find $\displaystyle P(2.5 \le X \le 7.5)$