Let X be a non-negative random variable. Find the PDF of the random variable Y=lnX for each of the following cases:

Question

For general fX, fY(y)=

Correct answer: fX(e^y)*e^y

2. When fX(x) = {1/4, if 2<x≤6,
0, otherwise,

we have fY(y) = {g(y), if a<y≤b,
0, otherwise.

Correct answer: g(y) = e^(y)/4
a= 0.6931
b= 1.7917

3. When fX(x) = {2(x−1), if 1<x≤2,
0, otherwise,

we have fY(y) = {g(y), if a<y≤b,
0, otherwise.

Correct answer: g(y)= 2*(e^y -1)*(e^(y))
a= 0
b= 0.6931