I) We live in dangerous times As I write this in November 2022, many people are worried that the world is on the brink of nuclear war. Just look at Google trends for the keyword, “probability”. The top related queries people are searching for involve this theme. Since the internet wants to know, I decided to…

I) Introduction You might have heard about the famous P=NP conjecture and the fact that there is a million dollar prize for proving or disproving it. It is concerned with the different problems we can encounter and how many of these we can solve with our computers and clever algorithms. There are…

Exploring higher dimensional objects with computer science algorithms — The applicability of graph theory in the context of web2.0 is obvious, with websites like Facebook (undirected graph of friendships) and Twitter (directed graph of followings) built around them. Another obvious application is in computer networks. The field of operations research, which started with applying math to the field of…

Or, the subtleties of two sample tests. — I) Contributing to popular repositories Making contributions to famous, open source repositories popular with practitioners in your field is a great way to demonstrate expertise. Being able to say, for instance: “if you use this method in SciPy, you’re using my code” is certain to get attention and make you stand out (we will be…

I) Introduction In warfare, having the biggest, most well equipped military means nothing if you can’t bring those forces to bear where you need them. Further, they need to be supported by a logistics network that provides a constant flow of things like fuel, food, spare parts for the equipment etc¹. The…

Many software products are meant to run on not just one, but a diverse set of environments. A website runs on many browsers, a software library like Numpy or Scipy runs on many operating systems and Python environments, software agents that run on the machines in a cloud system will…

Take a look at the probability density function of the F-distribution. — Here, B(.,.) is the Beta function. It turns out that this has a mean only when its d_2 parameter is >0, doesn’t matter what d_1 is. Moreover, when d_2 < 0, it ceases to be a valid distribution. You can reach all of these conclusions yourself by simply looking at…

A question inspired by an interview with a San Francisco-based startup — Say you have a coin and know nothing about the probability of heads. It’s reasonable to assume it’s distributed uniform between 0 and 1 (no reason to prefer any probability over any other since we haven’t seen any data). Now, you toss it 10 times and see 6 heads and…

People often use percentiles to summarize data. The median is the 50-th percentile and is known to be very robust to outliers in the data (as opposed to the mean). In addition, it represents a “typical sample” which the mean doesn’t necessarily. Sometimes, people feel they need to chase the…