Given a probability density function find the mean, median and mode of the distribution.
Get into the exponential distribution through an exploration of its pdf.
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?
Investigate the normal distribution
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.
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?