- A continuous random variable \(X\) has the cumulative distribution function
$$\begin{array} { l l }
\mathrm { F } ( x ) = 0 & x < 2 ,
\mathrm {~F} ( x ) = k ( x - a ) ^ { 2 } & 2 \leq x \leq 6 ,
\mathrm {~F} ( x ) = 1 & x \geq 6 .
\end{array}$$
- Find the values of the constants \(a\) and \(k\).
- Show that the median of \(X\) is \(2 ( 1 + \sqrt { 2 } )\).
- Given that \(X > 4\), find the probability that \(X > 5\).