Z = X/Y independant continuous random variables

In summary, the conversation is about finding the density function of Z, where Z = X/Y and X and Y are identical independent continuous random variables. The person is looking for resources to help them solve this problem.
  • #1
Barioth
49
0
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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  • #2
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

$\chi$ $\sigma$
 
  • #3
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

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FAQ: Z = X/Y independant continuous random variables

What is the definition of independent continuous random variables?

Independent continuous random variables are two or more variables that are not affected by each other and have a continuous probability distribution. This means that the outcome of one variable does not impact the outcome of the other variable, and both variables can take on any value within a given range.

How are the probabilities of independent continuous random variables calculated?

The probabilities of independent continuous random variables are calculated by multiplying the individual probabilities of each variable together. This is known as the multiplication rule for independent events.

Can the values of independent continuous random variables be correlated?

Yes, the values of independent continuous random variables can be correlated. This means that there may be a relationship between the variables, but this relationship does not affect their independence. Correlation only measures the strength and direction of the relationship between variables, not their independence.

What is the difference between independent and dependent continuous random variables?

The key difference between independent and dependent continuous random variables is that the values of dependent variables are affected by each other, while the values of independent variables are not. This means that the outcome of one variable can influence the outcome of the other in dependent variables, but not in independent variables.

Can the independence of continuous random variables be tested?

Yes, the independence of continuous random variables can be tested using statistical methods such as correlation analysis or chi-square tests. These tests can help determine if there is a relationship between the variables, and if so, the strength and direction of that relationship.

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