I'm a data scientist at Microsoft, in the ExP platform. We constantly interview and hire for other data scientists, and it's tough to get quality people.

With all the hotness around data science, it's inevitable that a bunch of schools are opening up special programs around data science, but the shit that most people forget to realize is that data science is built upon mathematics.

So if you don't know your fundamentals in math, then you're fucked. You can probably get away for a while producing some data porn, but in whatever soon-to-be-failed startup you join, you will get some data and end up describing it, even though the real value is in making useful conclusions from it.

It's tough to do an interview that involves actual data analysis in an on-site interview (some firms give homework-like exercises; we don't although I do like the idea) but let's go through some problems we ask and why we like them.

A bus runs every 15 minutes outside my apartment. If I come down at some random time, how long, on average, will I have to wait before I catch a bus?

Plenty of people I have interviewed can't even give me their intuition on what the answer is, which usually implies that the candidate is going home without a job offer.

Even for those that have the intuition for the answer, getting it rigorously is still problematic for most, because they can't comprehend what it means. What are we describing here? We have a certain amount of time we're waiting, and it's unknown. This is a random variable. In our scenario, this follows the uniform distribution $Unif(0, 15)$, and so once we are here we simply plug and play:

$$E[Unif(0, 15)] = \int_0^{15} x\left(\frac{1}{15}\right)dx$$

Check it out on Wolfram Alpha in case you can't do it yourself, but math don't lie: it's 7.5.

Okay - so this was only the warm-up for the actual problem. Next time - the real problem.