Foreverlasting's blog

Official website. Homework 1 Problem 1 (Expectation as the optimal estimator) Let XXX be a random variable with finite expectation. Show that the function f(a)=E(X−a)2f(a) = \mathbb{E}(X − a)^2f(a)=E(X−a)2 is minimized at a=EXa = \mathbb{E} Xa=EX. E(X−a)2=EX2−2aEX+a2=(a−EX)2.\mathbb{E}(X-a)^2=\mathbb{E}X^2-2a\mathbb{E}X+a^2=(a-\mathbb{E}X)^2. E(X−a)2=EX2−2aEX+a2=(a−EX)2. Problem 2 (Expectation of random vectors) Let XXX and YYY be random vectors in Rn\mathbb{R}^nRn. (a) (Linearity)...

Some random language… Tell a joke. The first time I learned that > is useful in Markdown. This May Day holiday made me feel like I’m getting closer and closer to a paramecium. Sigh… I really miss my childhood. Back then, I was immersed in a world of fantasy and never felt despair. Now, even though I still fantasize every day, I feel despair when I wake up. It feels like childhood was only better because I knew nothing. The more I learn and experience, the more I feel like...

I am terribly confused… If my contribution to recent academic work isn’t truly indispensable, then what is my purpose? Anyone could replace me. Why do I even exist? The solution I’ve come to now is to grow stronger… I need to start reading HDP again and struggle to learn English.

On April 2, 2025, in order to share some files between different devices, I had to free up some storage in iCloud. However, I mistakenly assumed the files were merely synced (not solely stored) in iCloud, so I deleted all the documents from it. As a result, all my local copies vanished! And because there were too many files, iCloud couldn’t restore them… I was in complete despair—until yesterday, when I discovered that my other MacBook still retained the previous iCloud files. This saved me.

This is the fourth time I’ve set up a personal blog, and each time, I feel more lost than before. I’m not entirely sure why I’m doing this again, but maybe the purpose—for now—is to push myself to keep learning. In the future, I’ll probably post mostly research-related or philosophical thoughts here…