- A continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \left\{ \begin{array} { l r }
0 & x < 2
\frac { 1 } { 20 } \left( x ^ { 2 } - 4 \right) & 2 \leqslant x \leqslant 4
\frac { 1 } { 5 } ( 2 x - 5 ) & 4 < x \leqslant 5
1 & x > 5
\end{array} \right.$$
- Calculate \(\mathrm { P } ( X > 4 )\)
- Find the probability density function of \(X\), specifying it for all values of \(x\).
- Find the value of \(a\) such that \(\mathrm { P } ( 3 < X < a ) = 0.642\)
- Find the probability density function of \(X\), specifying it for all values of \(x\).