2023 ACJC CA2 Q3

A random variable \(X\) has the probability distribution given in the following table.

1. Given that \(\mathrm{E}\left( \left| X-3 \right| \right)=1.8\), find the values of \(a\) and \(b\).[3]
2. Given that \({{X}_{1}}\) and \({{X}_{2}}\) are two independent observations of\(b\). \(X\), find \(\mathrm{P}\left( \left| {{X}_{1}}-{{X}_{2}} \right|=2 \right)\).[2]