[LatticeAnimal]

> Two points are randomly and uniformly selected on a line 0.0 to 1.0. What is the most probable distance between the two points?

Unless I am reading this wrong, I think all values between 0 and 1 have an equal probability (of 0).

The probability that a random uniform variable will equal any number between 0 and 1 is zero. It seems to follow that the probability of the difference between two uniform variables equaling any exact value would also be 0.

Have I missed something obvious? If zero really is the correct answer, that is pretty tricky.

[dmillar]

You have two random uniform variables and the distance/difference/change between to finite points.

Put another way (and code it up if you want). Select two random uniformly distributed points between 0 and 1. Do this 10_000 times, whats the average distance between the two?

This gets to the question of "most probable" vs "expected value". A conversation I always welcomed.