binomial

In doing so nothing goes wrong, and the binomial theorem becomes simple and convenient to state. Without defining 0!

With random data this should lead to a binomial distribution of block sizes centred around the target block size. But minimum and maximum block sizes are also enforced for pathological cases which skews this slightly.

This is a binomial distribution. Nice animation though.

Time for some fun with binomial probabilities! Assuming I interpret the actual problem at hand correctly, this is how we formulate it statistically.

From the article's example the simplicity of the binomial formula is extremely useful compared to a formula that would have to account for the case where k=0. Another commenter pointed out the useful elegance of 0log0=0 for physicists.

Otherwise, my initial response would be a visit to Wikipedia where my eyes would promptly glaze over at the text talking about "binomial coefficients" and I'd decide your job advertisement was misleading and it probably isn't a good job anyway. Assuming you terminated the interview first, I'd go home and come to resent you for asking such a deceptive question.

For example, the binomial cube, as good as it is, is still a fairly complex concept; a computer representation of it could extend it by allowing a student to reshape pieces in a 3D space, or provide values for the x, y and z variables and see how the cube transforms. This would allow for an even more powerful and intuitive understanding of how the pieces, sides and full cube relate to the binomial equation; and its manipulation that you could only do in a virtual environment.

Exponential family distributions include: poisson, exponential, bernoulli, multinomial, gaussian, negative binomial, etc.

I liked this but as other commenters have pointed out it's purely binomial at this stage. The great thing about the central limit theorem is that it is more general than just the limiting Binomial case.