1. (Markov's and Chebyshev's Inequality) a) Use Markov's inequality to show that for a sequence of positive random variables X1, X2, ... with values in N = {0, 1, 2, ...} and lim; 0 E[X;] = 0, it holds that lim;00 P[X; = 0] = 1. b) Use Markov's and Chebyshev's inequality to give two upper bounds on the probability that an exponential distributed random variable with parameter A (rate) is larger than x. Calculate the bounds explicitly for = 5 and x = 3,

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