## A Note on Conditional Probability

Posted on Sat 25 December 2021 in Mathematics • Tagged with Mathematics

$\newcommand{\cE}[2]{\mathbf{E}(#1\ |\ #2)}$$\newcommand{\cP}[2]{\mathbf{P}(#1\ |\ #2)}$$\renewcommand{\P}[1]{\mathbf{P}(#1)}$$\newcommand{\E}[1]{\mathbf{E}(#1)}$$\newcommand{\F}{\mathcal{F}}$$\newcommand{\G}{\mathcal{G}}$$\newcommand{\ind}[1]{\mathbf{1}_{#1}}$ To motivate this note, I’ll pose the following …

## A Note on Random Variables

Posted on Fri 03 December 2021 in Mathematics • Tagged with Mathematics

$\newcommand{\triple}{(\Omega, \mathcal{F}, \mathbf{P})}$$\newcommand{\P}{\mathbf{P}}$ This note on random variables follows as a result of confusing notation in several math textbooks. I'll explain random variables (in measure theoretic terms) as verbosely as I can, and then prove some results. This article assumes that the …

## Updates on Life in general

Posted on Sat 14 August 2021 in Writing • Tagged with Writing

I haven't done one of these in a year or so (this was the previous one), and neither have I written content exclusively for my blog for atleast a few months now, so it's a good time to do one of these because a lot has changed in the past …

## How it Happened

Posted on Mon 02 August 2021 in Writing • Tagged with Writing

"Baba, I got Mathematics and Computing Dual at IITD", I told my father excitedly on the day the first round allocations were over. "It probably won't change now". Certain of this, I returned back to whatever I was doing, excitedly waiting for the seat allocations to get over (while simultaneously …

## This summer

Posted on Wed 16 June 2021 in Writing • Tagged with Writing

What is a dream? all of us think of dreams as abstract ideals, far removed from reality, that we should chase with all the effort we can muster every day.

Meditating on this a bit more, does this make sense? What is achieved by chasing an ideal when you can …

## Setting up (and shifting to) Sublime Text 4

Posted on Tue 01 June 2021 in Programming • Tagged with Programming, Text Editor

After using vim for a long time, I realized that vim would be very tricky to use for larger projects; there are a few reasons behind this, which are:

1. Hard to set up and use autocomplete: I've tried omnicomplete, but it just didn't cut the mustard. I very seldom need …

## The Last Time

Posted on Sat 29 May 2021 in Writing • Tagged with Writing

Soft sunlight streaked in through the curtains, illuminating the room in a warm glow. Of course, I noticed none of that. The only thing I was aware of was my phone's alarm clock ringing. After drowsily hitting the snooze button, I realized that I had done this twice already, so …

## Function transforms (providing a broader picture of Laplace Transforms)

Posted on Wed 12 May 2021 in Mathematics • Tagged with Mathematics

A function is a mapping between two sets: the domain D and the codomain C.

It's very important to note here that the function is the mapping itself, and not an element in the codomain or the domain. The function …

## LaTeX primer

Posted on Sun 21 March 2021 in Programming • Tagged with Programming, Mathematics

This is a short getting started article on LaTeX; Recently, one of our courses involved a bit of LaTeX work, and this is meant to be a short introduction on how to use LaTeX to explain one's working.

## Getting Started

LaTeX (Pronounced lay-tech, stylized $\LaTeX$), at it's core, is merely …

## C development on a Mac

Posted on Thu 18 March 2021 in Programming • Tagged with Programming, C

C development on a Mac has it's fair share of traps and pitfalls, even though Mac is supposed to be POSIX compliant. I'll cover a few of them here, with the hope that nobody repeats the same mistakes :)

## XCode CLT Pitfalls

The first thing one does while starting out with …