Question 1 More on Probabilistic Inequalities. (See Midterm 2 Question 1]. [a] Prove Chemo's bound: For a random 1variable Y and constants a :> I]; I} I], my (3} etc. ' P(Y1'_>c.} g Prove this using Markov's Inequality. [b] Let Y N Unil), a = 1.T5 and t L} 0. Apply the ChernoE bound to P(Y 3 a) and minimize the upperbound with respect to t. (c) Let Y N U m" f [1,2], o. = 1.75. Apply Markovls inequality and Tchebyshef's Theorem to P(Y 2 a). [Hint: for Tchebyshelt's Theorem, you will need to do a little rewriting of the probability to match the statement of the theorem.) Cl Of the three up erbounds ill problems l3 and C which is the \"ti htest\" i-e- closest 130 P '.I g the actual probablhty)