Consider a small population consisting of N = 8 students with the following exam grades: Y, 72, Y-74, Y-76, Y-77, Y, 81, Y-84, Y, = 85, Y, -91 a) Compute the population mean y SY N b) Compute the population variance S 1 N-1 - . c) Identify all possible simple random samples of size 2. (There should be 28 possible samples, ignoring the order of selection.) Compute the mean of each possible sample y = 1/2(v, + y) and make a histogram of the sample means. 1 d) (i) Compute the sampling variance of the sample means obtained in c) by computing (v)=(-), where S is the number of samples of size n = 2 selected from the N = 8 elements in the population, and the s subscript represents the different samples. (ii) Compare this result to the estimated sampling variance (v) S. S the population element variance (iii) Compare this result to the sampling variance of the mean estimated directly from one sample realization of size n = 2.i.e., estimate of the SRS variance for the mean of samples of size n = 2 n v (y) = (1-1) s s=the element variance of y's in the sample realization of size n = 2. "