Part C: Let Y = 1 + 2X + u where X = Z1 + Z2, u = Z1 - Z2, Z, and Z2 are independent standard normals. We have iid observations (X,, Yo), from this model. (a) Suppose we run the following regression Yi = at Xip+ errorli to obtain the OLS estimator Borg- What would you expect the value of Borg to be when n - co? Please give a numerical answer. (b) Suppose we run the following regression X; = 6+ Y,y + error2; to obtain the OLS estimator Tors. What would you expect the value of fors to be when n - co? Please give a numerical answer.Part B: Let X1 and X2 be iid random variables with 2, with probability of 1 I? X; = i, with probability of 1ft G, with probability of 154 feri=1and2 1. What is the mean of Xi? What is the standard deviation of Kg? 2. What is the mean of fig = [X1 + X3} {2? What is its standard deviation?II 3. What is the distribution at is? graph the distributions at X1 and it. Is the distribution of X2 close to be normal? (hint: X2 can be regarded as the mean of a simple random sample with rePlaDEment from the population of four persons with their X 's equal to 2, 2,4, and B, respectively]