Random Variables - Continuous

Into the Exponential Distribution

Stage: 5 Challenge Level: Challenge Level:1

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

PDF

Stage: 5 Challenge Level: Challenge Level:1

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

What's Your Mean?

Stage: 5 Challenge Level: Challenge Level:1

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

pdf Stories

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Circle pdf

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

PCDF

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When can a pdf and a cdf coincide?

Scale Invariance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Exponential Intersection

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can the pdfs and cdfs of an exponential distribution intersect?

Normal Intersection

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore the intersection possibilities for normal pdfs.