In Homework 4 you found the expectation of each of the random variables below. \textbf{Go back and see how you did that, and then use the same ideas} to find the variance of each one. For one part you will need the fact that the SD of a geometric \((p)\) random variable is \(\frac{\sqrt{q}}{p}\) where \(q = 1-p\). We haven't proved that as the algebra takes a bit of work. We will prove it later in the course by conditioning. \textbf{(a)} A die is rolled \(n\) times. Find the variance of number of faces that \emph{do not} appear. \textbf{(b)} Use your answer to (a) to find the variance of the number of distinct faces that \emph{do} appear in \(n\) rolls of a die. \textbf{(c)} Find the variance of the number of times you have to roll a die till you have seen all of the faces