\"STABUUOY - Advanced Theory of Statistics\" is a graduate course taught at UTSG, which can only be taken by PhD students in the Department of Statistical Sciences. Assume the class consists of N = 8 students. The nal marks in the course are: 95, 66, 71, 93, 75, 88, 58, 100 [a] Find oz, the population variance. Show all the steps. Do not use any statistical paekagelexeel here. For example, do not copy the nal answer from R or from excel. Circle the final answer. {b} Based on a simple random sample (without replacement) of size 4 selected from this class, find the exact variance of the sample total. Show all the steps. Circle the final answer. [cl Based on a simple random sample [with replacement) of size 4 selected from this class, find the exact variance of the sample total. Show all the steps. Circle the final answer. {d} According to the graduate school, a student fails a course if a student scores less than 7 2. Based on a simple random sample (without replacement) of size 4 selected from this class, find the exact variance of the sample proportion of students who failed this course. Show all the N steps. Circle the nal answer. Hint: V) = 1:1_q (hf:11)