Given a probability density function find the mean, median and mode of the distribution.
What happens if this pdf is the arc of a circle?
Investigate the normal distribution
When can a pdf and a cdf coincide?
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 ?
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?
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 ?