"STA3000Y - 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 = 12...

Extracted text: "STA3000Y - 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 = 12 students with o² = 105. The final marks in the course are: 94, 65, 71, 92, 72, 78, 68, 96, 80, 91, 86, 79 Let ysy be the sample mean of a systematic random sample of size 3. Find the distribution (i.e., probability mass function) of ysy. You need to report the numerical values. Show all the steps. Circle the final answer. Find the exact value of E(ỹsy). You need to report the numerical value. Show all the steps. Circle the final answer. Find the exact value of V(ysv). You need to report the numerical value. Show all the steps. Circle the final answer.