In a probability distribution the random variable \(X\) takes the value \(x\) with probability \(kx^2\), where \(k\) is a constant and \(x\) takes values \(-2, -1, 2, 4\) only.

1. Show that \(P(X = -2)\) has the same value as \(P(X = 2)\).
2. Draw up the probability distribution table for \(X\), in terms of \(k\), and find the value of \(k\).
3. Find \(E(X)\).