Dear Wentao, Please consult https://sites.math.rutgers.edu/~zeilberg/Hist21/q2S.pdf for the full solutions. You got 5 points (out of 10). Good job! #1, #3, #4 is right. Next time you have to explain #4, but this time I did not take points off for that. You are welcome to come to my office hours (both on-line and in-person) Best wishes, Dr. Z.