User:HKIDz404520(4)

I am not a degree holder. I am just an amateur.

I have a little college level discover in Statistics.

It is a about finite population correction FPC($H_n^N$) factor.

I hope this little discover could help me to pursuit a degree and change my life. Thank thank everyone.

I am not tertiary educated. My background is worse.

I came from a grass-root family and my education history is full of grievance.

I faultily picked up art subjects and lost the chance to study science and math during my secondary education.

I was not eligible to the vocational training of any engineering field. Finally, I self-studied all the topics till the year-1 level.

Summary
Biased population variance $$V_r$$, sample variance $$V_n$$ and population variance$$ V[\bar{n}]$$ have following relations:

How to proof
The proof can be started by the expression similar to the proof of FPC($C_n^N$):

$$ H^n_r \sigma_\bar{x}^2 = \sum_{r=q}^n ... \sum_{k=j}^n \sum_{j=i}^n \sum_{i=1}^n (\frac{x_i + x_j + x_k...+ x_p + x_q + x_r}{r}-\mu) (\frac{y_i + y_j + y_k...+ y_p + y_q + y_r}{r}-\nu)$$