A stick of length 1 is broken into two pieces of length Y and 1−Y respectively, where Y is uniformly distributed on [0,1] . Let R be the ratio of the length of the shorter to the length of the longer piece.
Find the PDF fR(r) of R .
Hint:. What is the PDF of the length of the smaller piece? For 0<r<1,
fR(r)= ???
Find E[R] .
E[R]= ????
8 answers
E[R] = 1/3
fR(r)=
2/(r+1)^2
submitted
2(r+1)2
Find E[R] .
E[R]=
0.23
submitted
2/(r+1)^2
submitted
2(r+1)2
Find E[R] .
E[R]=
0.23
submitted
fR(r)= 2 / ((r + 1)^2)
1-2*(1-ln(2))
E(R)=ln(4)-1
1. fR(r)= 2/((r+1)^2)
2. E[R]= 0.38629436112
2. E[R]= 0.38629436112
why is fR(r) = 2/(r+1)^2 and not 1/(r+1)^2 ?? where does the 2 com from ??
ah ok, i thing i got it, 1-Y is once the shorter end and once the longer
1 answer