Question: Suppose that the number of tin cans recycled in a day at a recycling center is a random variable with an expected value of 50,000 and a variance of 10,000.
a) Use Markov's inequality (Exercise) to find an upper bound on the probability that the center will recycle more than 55,000 cans on a particular day.
b) Use Chebyshev's inequality to provide a lower bound on the probability that the center will recycle 40,000 to 60,000 cans on a certain day.
Exercise: Let X be a random variable on a sample space S such that X(s) ≥ 0 for all s ∈ S. Show that p(X(s) ≥ a) ≤ E(X)/a for every positive real number a. This inequality is called Markov's inequality.