1. (10 points) (Markov's and Chebyshev's Inequality) a) Use Markov's inequality to show that for a sequence of positive random variables X 1 , X 2, . . . with values in N = {0, 1, 2, . . } and liming) ]E[X%] = 0, it holds that limit-moo ]P'[Xz- = 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 an Calculate the bounds explicitly for A = 5 and :1: = 3