Concentration Inequalities: From Markov to Chernoff

A fair die is rolled $n = 600$ times. Let $S$ be the sum of all rolls. (a) Compute $E[S]$ and $\text{Var}(S)$. (b) Using Chebyshev's inequality, bound $P(|S - 2100| \geq 200)$. (c) Using the Central Limit Theorem, estimate $P(|S - 2100| \geq 200)$. (d) Using the Chernoff/Hoeffding bound, bound $P(S \geq 2300)$. (e) Which bound is tightest? Why?