The probability density of random variable x is
f(x)= 1
1/(2- 1)
=
1,
( 1 & lt; x & lt2);
0,
(others).
The inverse function h(y)=( 1/2)ln(y) of the function y = e (2x), and its derivative is h'(y)= 1/(2y). Therefore, the probability density ψ(y) of y is
ψ(y)
=f[h(y)]|h'(y)|
= 1/(2y),
(e^2
& lt
y
& lt
e^4);
0,
(others).