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).