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 …

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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 …

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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 …

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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 …

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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 …

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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 …

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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 …

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Function transforms (providing a broader picture of Laplace Transforms)

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

I'll begin this article by brushing up a few definitions:

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

function definition

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 …

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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 …

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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 …

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