Day 3

day 20 2 am, 3 January 2026 i woke up like 4 hours ago. hung out w the fam, read my day 16 goa blog (banger btw) and wasted some time now we’re finally starting the work! yuh man, life is fun, people around me are so supportive. just enjoy the process honestly, and do cool shit every single day. also one thing i want you to remember is; this is the only thing that matters to me. like MY WORK is the only thing that matters, apart from that nothing is that seriuos, like nothing else is like that deep, so just enjoy your life. anywyas; today what I wanna do is, I wanna speedrun probability. I’ll be doing Stirzakers probability book (which is good cos it doesnt do measure theoretic bs) and my aim is to complete the first 7 chapters before 11 am today. i mean yeah thats pretty much what ill be working on right now, and btw this attitude is perfect… just maximise the cooleness and the work done each day, literally nothing else matters, genuinely man. letsgo. 2:40 am ion even give a fuck. lets start now. 3:15 am well chapter 1 is done… there was nothing really interestnig here, just the basic definitions. the one sort of non trivial thing i did was if $A_1 \subseteq A_2 \subseteq \cdots … A$ then $P(A)=\lim_{n \to \infty} P(A_n)$ i mean yeah. apart from this nothing really interesting happened. ahhhh fuck i dont fucking know why im so distracted though, when i woke up i was js excited to work the whole night and learn cool shit. idk man, im telling you, please only focus on your work, everything else, everyone else, literally none of it matters please. just enjoy the work, and have fun every single day doing your best, right make every day legendary. apart from that, just enjoy life man, life is perfect, so many fun things to do in life, but its just fun. ok back to work then. 5:30 am lmao i was tripping. the truth is, we just gotta have fun man. yeahhhh leswork bruh. this is my life, lets enjoy it to the fullest. chapter 2 coming up:- 5:38 am chapter 2 done. im just kind of a genius lmao, it takes me very little time to udnerstand and internalise shit it seems like haha… just defined what probability distribution function was etc. etc. im trusting that i actually intuitively understand all this, not really focusing too much on the boring details; since this is a speedrun lmao. onto chapter 3 now. green day radio playing, this is genuinely so fun. i just feel so happy man tf. wowie bruh. 5:53 am ok there’s a bunch of terms here. remember what bern(p); binom(n,p) = x1+x2+..xn where each x is bern(p); poisson(t): f(k)= t^k/k! … ok remember what moments and central moments are. if x and y are independent; obv E(XY)=EX EY ; and these two vars are called uncorelated if E(XY)=E(X)E(Y) 6::00 am ok im just learning all the theory and assuming ill be able to do everything myself when i need to lmao. fair assumption but yuh this shits fun haha 6:08 am im at dependence now. gotta really understand this shit well. ill go a little slow here. 6:28 am wtf is this song, scotty doesnt know that fiona and me do it in my van every sunday lmao. wthell bruh. retards haha, fuck this haha. just have fun lmao. 6:35 am conditional expectation is cool. so if you have joint distribution; you can look at say f(Y|X); and you can calculate expectation of Y given X=x; this is obv a function of x; say h(x); this is the conditional expectation function; by double counting you can see E(h(x))=E(Y) and more generall E(h(x)g(x))=E(g(x)Y) for all g ; this is apparently another equivalent defintion of conditional expectation as the unique function for which this holds. 6:53 am read about polymarket a little. good news; its allowed in india lmaoooo. this is going to be my first like really cool project with users, gonna complete it before jan ends; polytok lesgo. anyways; starting chapter 4 now woohoo 7:30 am i just watched a bunch of clavicular edits, that nigga is soooo fucking inspiring bruh. thats the level of obsession im having bruh. lets wokr.