Answer:

The probability density of random variable X is

f(x)=

1/(2-1)< /p>

=

1,

(1

0,

(other) .

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

<

y

<

e ^4);

0,

(other).