The wait time for the first/next arrival follows an Exponential distribution. The wait time for the ‘r’th arrival () follows a Gamma distribution.

The probability density function of the Gamma distribution is derived using the convolution of individual random variables .

For increasing values of r, the distribution is like this.

It tends to look like a bell. Is it normal?

Nah, it may be a Gamma thing. Let me add uniform distributions.

For increasing values of *n*, the distribution of the sum of the uniform random variables is like this.

It tends to look like a bell. Is it normal?

Hmm. I think it is just a coincidence. I will check Poisson distribution for increasing values of . Afterall, it is a discrete distribution.

Tends to look like a bell. Is it normal?

Perhaps coincidence should concede to a consistent pattern. If this is a pattern, does it also show up in the Binomial distribution?

There it is again. It looks like a bell.

What is this? Is it normal?

The shape is limited to a bell. Is it normal?

It is the same for any variable. Is it normal?

Why is it normal?

What is the normal?

*To be continued…*

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