Problems 1. Probability Refresher. Let X be a random variable which is 1 with probability 1/100 and 0 with probability 99/100. (a) (2 points) What is the expected value E[X]? (b) Suppose you draw n independent random variables X1,X2, .,Xn, distributed like X. (i) (2 points) What is the probability that X,-1 AND Xs = 1? (ii) (2 points) What is the probability that xi equals n? (iii) (2 points) What is the expected value E ? (Hint: use linearity of expecta- tion) iv) (2 points) Suppose now we change only the distribution of X such that it comes up I with probability 1/2 and 0 with probability 1/2. The rest of the X still remain the same as X. What is now EX