Suppose that \(X \in \{1,2,3\}\) and \(Y = X+ 1\), and \(\mathbf{P}(X = 1) = 0.3, \ \mathbf{P}(X = 2) = 0.5,\ \mathbf{P}(X = 3) = 0.2.\)

(a) Find \(\mathbf{E}(X)\).

(b) Find \(\mathbf{E}(Y)\).

(c) Find \(\mathbf{E}(X + Y)\).

[Author Mark Huber. Licensed under Creative Commons.]