Can the pdfs and cdfs of an exponential distribution intersect?

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.

Explore the intersection possibilities for normal pdfs.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Can you work out the means of these distributions using numerical methods?

Invent scenarios which would give rise to these probability density functions.