2. Collecting Distinct Values In Homework 4 you found the expectation of each of the random variables below. 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 random variable is where . We haven't proved that as the algebra takes a bit of work. We will prove it later in the course by conditioning. (a) A die is rolled times. Find the variance of number of faces that do not appear. (b) Use your answer to (a) to find the variance of the number of distinct faces that do appear in rolls of a die. (c) Find the variance of the number of times you have to roll a die till you have seen all of the faces