Let f(x)=x/8 be the density of X on [0,4], zero elsewhere.
a) Show that f(x) is a valid density and compute E(X)
b) Define Y=1/X. Calculate E(Y)
c) Determine the density function for Y
The Attempt at a Solution
a) is just really basic. I've solved that one.
b) Without any "fuss" about it, i set g(x)=1/x, and use the following formula
[itex]\int^4_0(1/x*x/8)[/itex] = 1/2
c) Here the problem starts... So from my lecture notes i know that
Y=1/X --> X=1/Y=g^-1(y)
Using this i can write the above as
the pdf is then:
From here, I do not know how to proceed, any clues?