Let X1 and X2 be iid random variables with Xi = 8 < : 2; with probability of 1/2 4; with probability of 1/4 6; with probability of 1/4 for i = 1 and 2: 1. What is the mean of Xi? What is the standard deviation of Xi? 2. What is the mean of X2 = (X1 X2) =2? What is its standard deviation? 3. What is the distribution of X2? Graph the distributions of X1 and X2: Is the distribution of X2 close to be normal? Hint: X2 can be regarded as the mean of a simple random sample with replacement from the population of four persons with their Xs equal to 2; 2; 4; and 6, respectively. The distribution should be similiar to