Compare the conditional distributions with the marginal distribution if the lab finds a way to eliminate the oldest cells (those >3 days old) from its stock.
Recall the cells in Section 6.4, Exercises 31 and 32. New cells stain properly with probability 0.95, 1-day-old cells stain properly with probability 0.9, 2-day-old cells stain properly with probability 0.8, and 3-day-old cells stain properly with probability 0.5. Suppose
Pr(cell is 0 days 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.
In each of the following cases, define two random variables, draw the joint distribution, find the marginal probability distributions, and compute and graph the conditional probability distributions for cell age. Compare the conditional distributions with the marginal distribution.