Z = X/Y independant continuous random variables

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SUMMARY

The discussion centers on finding the density function of Z, defined as the ratio of two identical independent continuous random variables X and Y. The user seeks guidance on the methodology to derive this density function, indicating a need for resources or lectures on the topic. Key references include the Wikipedia page on ratio distributions, which provides foundational knowledge on the subject. The inquiry highlights the importance of understanding the properties of independent continuous random variables in probability theory.

PREREQUISITES
  • Understanding of independent continuous random variables
  • Familiarity with probability density functions
  • Knowledge of ratio distributions
  • Basic skills in mathematical statistics
NEXT STEPS
  • Study the derivation of the density function for the ratio of two independent continuous random variables
  • Explore the concept of ratio distributions in depth
  • Review resources on probability theory, focusing on continuous random variables
  • Learn about the transformation techniques in probability distributions
USEFUL FOR

Students of statistics, mathematicians, and anyone interested in probability theory, particularly those studying the behavior of ratios of random variables.

Barioth
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Hi,

Let's say I'm given X and Y identical independent 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 independent 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 independent 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

.
 

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