12.4 Exercise 9

The class $\left\{A , B , C , D , E , F\right\}$ is independent, with respective probabilities

0.43, 0.53, 0.46, 0.37, 0.45, 0.39. Let

1. Use properties of expectation and variance to obtain $E \left[X\right]$, $Var \left[X\right]$, $E \left[Y\right]$, and $Var \left[Y\right]$. Note that it is not necessary to obtain the distributions for X or Y.
2. Let $Z = 3 Y - 2 X$.
   Determine $E \left[Z\right]$, and $Var \left[Z\right]$.