- #1

- 51

- 0

## Homework Statement

Let X be a random number from (0,1). Find the probability density function of Y = 1/X.

## Homework Equations

## The Attempt at a Solution

I keep thinking this is easier than I am making it out to be, but the only places I find anything similar searching is on two exams at two different schools, so it must be more interesting than I thought.

I am attempting to first find the distribution function and then differentiate to get the density function (not sure that is the right way to approach)

for any x between 0 and 1, the probability distribution would be

0 if x < 0

x if 0 [tex]\leq[/tex] x < 1

1 if x [tex]\geq[/tex] 1

for y = 1/x

x = 1/y

so F(y) = 1/y and F'(y) = f(y) = -1/[tex]y^{2}[/tex]

I know the answer is 1/[tex]y^{2}[/tex] and not negative, but I have the suspicion that I am doing it wrong anyway and my answer is just coincidentally close to correct. Please help