Investigate the normal distribution
Get into the exponential distribution through an exploration of its pdf.
What happens if this pdf is the arc of a circle?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
When can a pdf and a cdf coincide?
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 ?
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.
Can the pdfs and cdfs of an exponential distribution intersect?