Define the function of density of the random variable Y.

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SUMMARY

The discussion focuses on defining the probability density function (PDF) of the random variable Y, which is selected from a uniform distribution on the interval (-1, x^2) where X is uniformly distributed over (-1, 2). Participants clarify that to find the PDF of Y, one must first assume a specific value for X and then derive the PDF accordingly. Additionally, computing the cumulative density function (CDF) of both X and Y is suggested as a more intuitive approach to understanding the relationship between these variables.

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jeka131404
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We selected X point from interval (-1,2). If X=x, we selected point Y from (-1,x^2). Define the function of density of the random variable Y.
 
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jeka131404 said:
We selected X point from interval (-1,2).
I think you mean that we selected X from a uniform distribution on the intervald (-1,2).

If X=x, we selected point Y from (-1,x^2).

I think you mean that Y is selected from a uniform distribution on (-1, x^2)


Define the function of density of the random variable Y.

I think you mean "Find the probability density function of the random variable Y".

To start your work, pretend X is given and state the probability density function for Y on the interval (-1,x^2). Can you do that?
 
What ST said makes sense. Another way is to try to compute the cumulative density function of X, and then of Y. This may be a bit more intuitive, since the CDF describes the probability of a specific event.
 

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