Probability density functions

$\pdf stories$

problem
PDF stories

Age

16 to 18

Challenge level

Invent scenarios which would give rise to these probability density functions.
problem
Into the exponential distribution

Age

16 to 18

Challenge level

Get into the exponential distribution through an exploration of its pdf.
problem
Distribution differences

Age

14 to 16

Challenge level

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
$Circle \pdf$

problem
Circle PDF

Age

16 to 18

Challenge level

What happens if this pdf is the arc of a circle?
problem
Into the normal distribution

Age

16 to 18

Challenge level

Investigate the normal distribution
problem
PCDF

Age

16 to 18

Challenge level

When can a pdf and a cdf coincide?
problem
Scale invariance

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Given a probability density function find the mean, median and mode of the distribution.
problem
Exponential intersection

Age

16 to 18

Challenge level

Can the pdfs and cdfs of an exponential distribution intersect?