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Problem 1: Web Traffic (25 points) A very unpopular math blogger is trying to drive more traffic to their website. The site analytics say that on average, they get about 15 visitors per hour. Let X be a random variable to represent the # of site visitors on a given hour. Assume all visits occur independently. (Hint: Use X ~ Poisson()). Look up the meaning of a Poisson r.v. as well as E[X] and Var(X) which you will need for this problem) 1. Use Markov's Inequality to come up with an upper bound on the probability that, on any given hour, the site gets 100 or more visitors 2. Use Var(X) and Chebyshev's Inequality to come up with a lower bound on P(10