The problem involves finding the density function of the random variable U^2, where U is uniformly distributed on the interval [−1, 1]. Participants are exploring the implications of this transformation on the boundaries of the distribution.
The discussion includes attempts to clarify the boundaries for U^2 and whether the derived limits are accurate. Some participants express uncertainty about their calculations, while others confirm the boundaries as being from 0 to 1.
There is a focus on the implications of the uniform distribution's limits on the transformation to U^2, with participants questioning how these affect the density function.
I like Serena said:Hi number0!
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.
number0 said:
I like Serena said:
