Probability density functions

problem
Favourite

Into the Exponential Distribution

Age

16 to 18

Challenge level

1 out of 3

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

PCDF

Age

16 to 18

Challenge level

2 out of 3

When can a pdf and a cdf coincide?
problem
Favourite

Into the Normal Distribution

Age

16 to 18

Challenge level

2 out of 3

Investigate the normal distribution
problem
Favourite

Scale Invariance

Age

16 to 18

Challenge level

3 out of 3

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

Distribution Differences

Age

14 to 16

Challenge level

2 out of 3

How could you compare different situations 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

2 out of 3

What happens if this pdf is the arc of a circle?
$\pdf stories$

problem

PDF Stories

Age

16 to 18

Challenge level

2 out of 3

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

Exponential Intersection

Age

16 to 18

Challenge level

3 out of 3

Can the pdfs and cdfs of an exponential distribution intersect?
problem

PDF

Age

16 to 18

Challenge level

3 out of 3

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