Problem 4 We have three balls which are labelled with 1,2 and 3 in our population. (Three balls are the same except label) The population parameter we interest in is a, the population mean. Let X = the number on ball. Therefore, our population mean is p, = 1'%' 2 2. For each pick, X follows a discrete distribution with sample space S = {1, 2, 3}, the distribution table is ramI Il 2 3 P(X=k) , %|% Now we want to take samples with size n = 2, that is, pick twice. ( each time we take a ball, we will replace it. For example, if I take 1 at the rst time, it is still possible for me to pick 1 at the second time. So each pick is independent.) One prisS'Ihle sample wilt size "=2 99 Population 00 Here are 3*3=9 samples in total 1. Give a frequencies plot or a barplot of our sample mean. 2. Is the sampling distribution of sample mean from part 1 normal? Why or why not