Thank you for your reply!
For question 4, I find out that it is a range not a single value. I did find my blind spot from the reply of Andrea Groude.
For question 5,may I ask what is the literature name?I really want to understand it more deeply.I don't care how complex it is and I am very willing to understand it totally.
Although there are many recommended book titles on the IFOA website, I really don't know where is it. When entering CS2, it is not as easy to find the correct information from the Internet as CS1.
I saw other definitions of CLT on the Internet: the distribution of anything tends to N(0,1) under large samples, so I though r~N(0,1) here,too.
I saw the numerator being divided by n-j and the denominator being divided by n, and I mistakenly thought that's why the variance was transformed from the variance formula of joint distribution of CS1 to 1/n.
Thank you for your response that made me realize I still need to find the exact source of information to make sure it's correct.
Last edited: Aug 21, 2023