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

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1. Nov 8, 2015

### whitejac

1. The problem statement, all variables and given/known data
Given a Uniform Distribution (0,1) and Z = X/Y
Find F(z) and f(z)

2. Relevant equations

3. 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...

2. Nov 8, 2015

### vela

Staff Emeritus
Did you mean
$$\lim_{z \to \infty} P(Z≤z) = 1?$$ If so, what's the problem with that?

3. Nov 8, 2015

### LCKurtz

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?

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

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