12 A random variable \(X\) has probability distribution defined as follows.
$$\mathrm { P } ( X = x ) = \begin{cases} k x & x = 1,2,3,4,5 ,
0 & \text { otherwise, } \end{cases}$$
where \(k\) is a constant.
- Show that \(\mathrm { P } ( X = 3 ) = 0.2\).
- Show in a table the values of \(X\) and their probabilities.
- Two independent values of \(X\) are chosen, and their total \(T\) is found.
- Find \(\mathrm { P } ( T = 7 )\).
- Given that \(T = 7\), determine the probability that one of the values of \(X\) is 2 .