Assume an ii d. sample from a population, and assume that both mean and variance of X exist. Use your knowledge of asymptotic distribution theory to find the probability limits and/or asymptotic distributions of the following expressions: 1 sigma_i=1^n X_i 1 sigma_i=1^n 1 X_i 1+12 sigma_i=1^n X_i (1 sigma_i=1^n X_i)^2 1 sigma_i=1^n X_i^2 1 - 1 sigma_i=1^n (X_i - X bar)^2/1 sigma_i=1^n X_i - X bar^2 n/12 sigma_i=1^n X_i 1/4 squareroot n sigma_i=1^n (X_i - mu_X)