5 ms·
Typically you would do a uniform (-x, x) and then take the limit. This isn’t necessarily the same as the (-1, 1) version though
by zeroonetwothree 2y ago
Typically you would do a uniform (-x, x) and then take the limit.
This isn’t necessarily the same as the (-1, 1) version though
- eigenket 2y agoIts the same because the uniform distribution over (-x,x) can be obtained by taking a random variable uniformly distributed over (-1,1) and multiplying it by x. This doesn't change anything for the question about roots because the roots of a polynomial don't change when you multiply it by x.
- thaumasiotes 2y ago> Typically you would do a uniform (-x, x) and then take the limit. But this is completely uninformative for the interval (-inf, +inf). Taking limits is a tool you can use, and it works well when the infinite behavior matches the limit of the finite behavior. The opposite is the case here and the infinite behavior is radically unlike the finite behavior. You might as well try to determine the value of an impulse function at zero by seeing what the limit is as you approach zero.