Invent scenarios which would give rise to these probability density functions.

When five dice are rolled together which do you expect to see more often, no sixes or all sixes ?

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 pdf.

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?

Can the pdfs and cdfs of an exponential distribution intersect?

Given a probability density function find the mean, median and mode of the distribution.