Given a probability density function find the mean, median and mode
of the distribution.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Get into the exponential distribution through an exploration of its
This problem is a good vehicle for fostering thinking about probability density functions and getting some talk into the statistics classroom. It could be used alongside a traditional introduction to the concepts to probability density functions or as a discussion-based consolidation. It can be approached from various levels of sophistication: all
students should be able meaningfully to engage with it, and you can come back to the ideas at several points during a course of statistics.