Suppose
Pr(cell is 0 day old) = 0.4
Pr(cell is 1 day old) = 0.3
Pr(cell is 2 days old) = 0.2
Pr(cell is 3 days old) = 0.1.
Consider again the cells in Section 6.4, Exercises 31 and 32, but suppose that older cells, instead of not staining as often, do not stain as well. New cells have a brightness of 9.5, 1-day-old cells have a brightness of 9.0, 2-day-old cells have a brightness of 8.0, and 3-day-old cells have a brightness of 5.0. Write a random variable describing the brightness, and find its probability distribution and its expectation.