Diving in Covariance and Variance from an idea of building a Virtual Teaching Assistant

I have ideas and sometimes those ideas with limited knowledge supports. In order to make something happen. My advisor, Yue recommend me to learn "Covariance and Variance". Yue threw me a question like below. He asked X is n by n matrix, what Y is.

I have no concept what the symbol X with a bar on the top and what the X' represents!!!

So, I start my journey to learn standard deviation...

Standard Deviation: mathematical symbols [sigma] 𝝈

Whisper: 为什么我们要学“方差”？什么是“差”？事件是可以测量的吗？我们可以预测未来吗？什么是“正常现象”？什么是”少数显现“？到底偏离正常多少，我们可以预测吗？如果98%都是可以预测的，那么我们是不是就可以成为“先知”？如果你说，你害怕预测未来，那个未来还是要发生吗？如果发生我们该怎么办？

BTW，平方是想让这个“差”，更明显！？

在统计学中，方差是用来度量单个随机变量的离散程度，而协方差则一般用来刻画两个随机变量的相似程度，其中，方差的计算公式为：

If I cannot apply this function or concept to approach to my idea, I may never can understand and remember it at all. Since I need to predict "students intent", I need to figure out the students speech and intent? To what extent a specific "word" relate a clean "intent"? How to calculate it? with I should say I need to better understand how computer predict students practical intentions.

Here I found a video. I like the design and animation. Here you go:

The intuition tells me those concept will help...

(5/21 is my due day to tell my story to Yue) !!!!!!!!