Blog

These articles cover topics in EE126: Probability and Random Processes which I took Spring 2018 under Professor Kannan Ramachandran. Over the last two years I've been very fortunate to work in the BAIR research lab - these problems are inspired from my time there!

## The Probability Bowl

The EECS + Math departments decide its time to hold a competition to see who knows their probability chops the best. Exciting!! The first round is divided into 3 groups. The top 3 finishers in each group are awarded finalist medals - the top finisher moves on to the final round. The final round consists of one ‘Problem of the Gods’. The time it takes you to finish the problem (if you can) determines the winners. Two of my friends and I are jokesters and make a bet that we’ll sweep the competition placing 1st, 2nd and 3rd in a certain order. Can we compute the probability that we do?

January 17, 2019

## Pick up hobbies?

Who needs hobbies when you can work all day? :) Unfortunately, perhaps, we aren’t yet machines. Let’s say you pick up a new hobby whenever you meet someone interested in it. If interesting, new people appear in your life randomly and independently and you spend a random amount of time on each hobby, by the end of a year how long would you have spent on hobbies? Also as fun as hobbies sound, you’re slightly concerned you might get carried away - what’s the probability you spend over 1000 hours in a year?

January 08, 2019

## I'm Popular!!

In the alternate universe of my dreams, I get to answer questions about probability! Wow! I’m beyond flattered. At first there are only two people, but soon more people start to join. I’ll wake up happy if I can finish answering each of their questions. What’s the expected amount of time until there are \(n\) people in line?

January 07, 2019

## Where lunch?

People arrive independently and at random times to work in the research lab. From observation, I’ve come to expect that \(\lambda\) people arrive there to work per hour. On a given day, everyone there decides to get lunch at one of the \(m\) restaurants nearby. We can’t unanimously decide on a place to eat so we each choose where to eat independently. If each of us has an equal probability of going to each restaurant, can we figure out the expected number of different restaurants we cover as a group?

December 30, 2018

## Debug Faster Please..

My three friends and I have only 5 more hours to finish debugging our last and final OS project. We’ve been working on it for over 16 hours non stop and all we want is to get the last test case to pass. We take a moment to be meta about our situation. If each of us has our own “bug fixing” rate and we team up to tackle different parts of the project, is finishing realistic? Can we actually compute the expected time it’ll take us to complete the project?

December 20, 2018

## The Music of Work

I love listening to music while I work, but often times I find myself listening to the same songs over and over again. If I replace my playlist with some probability every day, how many days can I expect my playlist to last?

December 15, 2018