5 Alana and Ben work for an estate agent. The joint probability distribution of the number of houses they sell in a randomly chosen week, \(X _ { A }\) and \(X _ { B }\) respectively, is shown in the table.
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1. Find \(\mathrm { E } \left( X _ { A } \right)\) and \(\operatorname { Var } \left( X _ { A } \right)\).
2. Determine whether \(X _ { A }\) and \(X _ { B }\) are independent.
3. Given that \(\mathrm { E } \left( X _ { B } \right) = 1.15 , \operatorname { Var } \left( X _ { B } \right) = 0.8275\) and \(\mathrm { E } \left( X _ { A } X _ { B } \right) = 1.09\), find \(\operatorname { Cov } \left( X _ { A } , X _ { B } \right)\) and \(\operatorname { Var } \left( X _ { A } - X _ { B } \right)\).
4. During a particular week only one house was sold by Alana and Ben. Find the probability that it was sold by Alana.