3 In a probability distribution the random variable \(X\) takes the value \(x\) with probability \(k x ^ { 2 }\), where \(k\) is a constant and \(x\) takes values \(- 2 , - 1,2,4\) only.
- Show that \(\mathrm { P } ( X = - 2 )\) has the same value as \(\mathrm { P } ( X = 2 )\).
- Draw up the probability distribution table for \(X\), in terms of \(k\), and find the value of \(k\).
- Find \(\mathrm { E } ( X )\).