ACJC DRV Tutorial Q4

The probability distribution of a discrete random variable \(X\) is as follows:

Find \(\mathrm{Var}\left( X \right)\).

The random variable \(Y\) is defined by \(Y={{X}_{1}}-{{X}_{2}}\), where \({{X}_{1}}\), \({{X}_{2}}\) are two independent observations of \(X\).

Find the probability distribution of \(Y\).

Verify that \(\mathrm{Var}\left( Y \right)=\mathrm{Var}\left( {{X}_{1}} \right)+\mathrm{Var}\left( {{X}_{2}} \right)\).