7. A continuous random variable \(X\) has the probability density function
$$\begin{array} { l l }
\mathrm { f } ( x ) = \frac { 6 x } { 175 } & 0 \leq x < 5
\mathrm { f } ( x ) = \frac { 6 x ( 10 - x ) } { 875 } & 5 \leq x \leq 10
\mathrm { f } ( x ) = 0 & \text { otherwise }
\end{array}$$
- Verify that f is a probability density function.
- Write down the probability that \(X < 1\).
- Find the cumulative distribution function of \(X\), carefully showing how it changes for different domains.
- Find the probability that \(2 < X < 7\).