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

  1. Nov 8, 2015 #1
    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. jcsd
  3. Nov 8, 2015 #2

    vela

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    Did you mean
    $$\lim_{z \to \infty} P(Z≤z) = 1?$$ If so, what's the problem with that?
     
  4. Nov 8, 2015 #3

    LCKurtz

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    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##.
     
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