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.
Investigate the normal distribution
What happens if this pdf is the arc of a circle?
When can a pdf and a cdf coincide?
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.
Can the pdfs and cdfs of an exponential distribution intersect?
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?