# Random Variables - Continuous

### Into the Exponential Distribution

##### Stage: 5 Challenge Level:

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

### PDF

##### Stage: 5 Challenge Level:

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

##### Stage: 5 Challenge Level:

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

### pdf Stories

##### Stage: 5 Challenge Level:

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

### Circle pdf

##### Stage: 5 Challenge Level:

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

### PCDF

##### Stage: 5 Challenge Level:

When can a pdf and a cdf coincide?

### Scale Invariance

##### Stage: 5 Challenge Level:

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:

Can the pdfs and cdfs of an exponential distribution intersect?

### Normal Intersection

##### Stage: 5 Challenge Level:

Explore the intersection possibilities for normal pdfs.