Kash Chandran

Well - it depends what you mean by that. I get this question every time I teach probability, so I figured I'd put it and its answer out there for everyone once and for all. "Why do we use probability density functions (pdfs) for continuous distributions and probability mass functions (pmfs) for discrete distributions?" Put another way, "Why can't we use pmfs for both discrete and continuous distributions?" For those of you who are with me up to here, the answer is that an uncountable sum of...

There was this Mensa IQ  question I saw back when I was 16. "Fill in the blank" it asked, It's one of the earliest problems that got me to jump down the math rabbit-hole, so I'm happy to share the solution here with you today, its intuition, and perplexing ramifications. First: the pattern. It's the surface area, and then volume of an n-dimensional sphere with radius r, starting from 0 dimensions (first 2 terms), 1 dimension (second 2 terms) and 2 dimensions (last 2 terms). What about the...

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