# Finding the PDF and CDF of a given function Z = X/Y

## Homework Statement

Given a Uniform Distribution (0,1) and Z = X/Y
Find F(z) and f(z)

## The Attempt at a Solution

So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it.
R(z) = {0,∞} because as y is very small, Z becomes very big.
After that, I'm not quite sure though because that would mean that P(z) would be 1 for z > ∞, and that doesn't make much sense...

## Answers and Replies

vela
Staff Emeritus
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## Homework Statement

Given a Uniform Distribution (0,1) and Z = X/Y
Find F(z) and f(z)

## The Attempt at a Solution

So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it.
R(z) = {0,∞} because as y is very small, Z becomes very big.
After that, I'm not quite sure though because that would mean that P(z) would be 1 for z > ∞, and that doesn't make much sense...
Did you mean
$$\lim_{z \to \infty} P(Z≤z) = 1?$$ If so, what's the problem with that?

LCKurtz
Science Advisor
Homework Helper
Gold Member

## Homework Statement

Given a Uniform Distribution (0,1) and Z = X/Y
Find F(z) and f(z)

Apparently you haven't given us everything you know. Are X and Y both uniform distributions on (0,1)? Are they given to be independent?

## The Attempt at a Solution

So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it.
R(z) = {0,∞} because as y is very small, Z becomes very big.

Best not to use set notation for intervals. I suppose you mean ##R(z) = (0,\infty)##, which would be the correct range.

After that, I'm not quite sure though because that would mean that P(z) would be 1 for z > ∞, and that doesn't make much sense...

What does P(z) mean? I agree, ##z>\infty## makes no sense. You would expect the cumulative distribution function to approach 1 as ##z\to\infty##.