2. A continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \begin{cases} 0 , & x < - 2
\frac { x + 2 } { 6 } , & - 2 \leqslant x \leqslant 4
1 , & x > 4 \end{cases}$$
- Find \(\mathrm { P } ( X < 0 )\).
- Find the probability density function \(\mathrm { f } ( x )\) of \(X\).
- Write down the name of the distribution of \(X\).
- Find the mean and the variance of \(X\).
- Write down the value of \(\mathrm { P } ( X = 1 )\).