2023 VJC P2 Q5

A discrete random variable \(X\) has the following probability distribution:

\(\mathrm{P}\left( X=r \right)=kr\), \(r=1\), \(2\), \(3\), \(4\), \(5\), \(6\),

where \(k\) is a constant.

1. Show that \(k=\frac{1}{21}\).[2]
2. Find the value of \(\mathrm{E}\left( X \right)\).[2]