Copyright © University of Cambridge. All rights reserved.

## 'Scale Invariance' printed from http://nrich.maths.org/

Don't forget that probability distribution functions must integrate
to $1$ over the allowed range of values.

Try changing variables for the first part.

For the second part, note that clearly $x^2\rightarrow (ax)^2 \neq
a(x^2).$

How could you make the two sides match for other powers of
$x$?