Suppose that X is uniformly distributed on the interval [3,8] , and that given X=x , Y is uniformly distributed on the interval [0,x] . That is, the conditional PDF of Y given X=x is

Question

fY|X(y|x)=1/x, 0≤y≤x.
Find the PDF fY(y) of Y . It will take the form

fY(y)=⎧⎩⎨aln(b) y∈[d,e]
aln(c/y) y∈[e,f]
0 otherwise.
Answer by finding a,b,c,d,e,f , where d<e<f .

Recall: If 0≤a<b, then ∫ba 1/x dx=ln(ba) .

(Enter your answers as fractions, or decimals accurate to at least 4 decimal places.)

a=
unanswered
b=
unanswered
c=
unanswered
d=
unanswered
e=
unanswered
f=
unanswered