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 ?
Given a probability density function find the mean, median and mode of the distribution.
Investigate the normal distribution
Can the pdfs and cdfs of an exponential distribution intersect?
When can a pdf and a cdf coincide?
What happens if this pdf is the arc of a circle?
Invent scenarios which would give rise to these probability density functions.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.