### Scale Invariance

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

### Into the Exponential Distribution

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

### PCDF

When can a pdf and a cdf coincide?

# PDF

##### Stage: 5 Challenge Level:
A variable $X$ is distributed in the interval $\{x:0 \leq x \leq 3\}$ according to the probability density function $$\rho(x) = {2\over 27}\big(6+x-x^2\big)$$ Find the mean, the median and the mode of the distribution.