Probability

The probability distribution of a discrete random variable \(X\) is given by

\(P(X = x) = \frac{x^2}{14}, x \in \{1, 2, k\},\) where \(k > 0\).

1. Write down \(P (X = 2)\).

   [1]

2. Show that \(k = 3\).

   [4]

3. Find \(E(X)\).

   [2]