MHB Z = X/Y independant continuous random variables

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The discussion centers on finding the density function of Z, defined as the ratio of two independent continuous random variables X and Y. The original poster seeks guidance on how to derive this density function and expresses uncertainty about the appropriate search terms for further research. Participants suggest looking into resources like the Ratio Distribution on Wikipedia for relevant information. The conversation highlights the need for clear methods to approach problems involving the division of random variables. Overall, the thread emphasizes the importance of understanding the properties of ratios in probability theory.
Barioth
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Hi,

Let's say I'm given X and Y identical independant continuous random variables.

We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)

If someone could redirect me to some lecture about this kind of problem I would be very happy!

Thanks for passing by
 
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Barioth said:
Hi,

Let's say I'm given X and Y identical independant continuous random variables.

We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)

If someone could redirect me to some lecture about this kind of problem I would be very happy!

Thanks for passing by

http://www.mathhelpboards.com/f52/unsolved-statistics-questions-other-sites-932/index4.html#post5581

Kind regards

$\chi$ $\sigma$
 
Barioth said:
Hi,

Let's say I'm given X and Y identical independant continuous random variables.

We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)

If someone could redirect me to some lecture about this kind of problem I would be very happy!

Thanks for passing by

Ratio distribution - Wikipedia, the free encyclopedia

.
 
Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...

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