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### Number and algebra

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### Probability and statistics

### Working mathematically

### For younger learners

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### Scale Invariance

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Age 16 to 18

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.

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

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