Example 6: Linear Combinations and Variance

Let X be the discrete variable with the following probability distribution. Calculate (a) E(X), (b) E(X^2), (c) E(4X+3), (d) E(2X^2+X-1), (e) V(X), (f) V(5X+4). \\[0.5em] \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline f(x) & \frac{2}{9} & \frac{3}{9} & \frac{1}{9} & \frac{3}{9} \end{array}