If U is uniform on [−1, 1], find the density function of U^2.

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Homework Statement



If U is uniform on [−1, 1], find the density function of U^2.


Homework Equations



f(u) = 1/(b-a)


The Attempt at a Solution



I actually solved the problem already, but I am having trouble defining what the boundaries are for U^2. My work is uploaded in paint.

Any help would be appreciated. Thanks.
 

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Answers and Replies

  • #2
I like Serena
Homework Helper
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Hi number0! :smile:

The integral in your solution runs from -√x to +√x, but that is only true if they are within the bounds of your uniform distribution.
If they are outside, you have values of x for which your integral bounds need to be modified, which in turn will result in other values for your density function.

If you do this, you will find your boundaries for U^2 implicitly.
 
  • #3
104
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Hi number0! :smile:

The integral in your solution runs from -√x to +√x, but that is only true if they are within the bounds of your uniform distribution.
If they are outside, you have values of x for which your integral bounds need to be modified, which in turn will result in other values for your density function.

If you do this, you will find your boundaries for U^2 implicitly.

I do not know if I did it correctly, but in my solution, I got the boundaries to be 0 < X <= 1. Is this correct?
 
  • #4
I like Serena
Homework Helper
6,577
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I do not know if I did it correctly, but in my solution, I got the boundaries to be 0 < X <= 1. Is this correct?

Yes.
 
  • #5
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0

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