4 ms·
There is no such thing as a uniform distribution over (-inf, +inf) for the simple reason that the Lebesgue measure of (-inf, +inf) is +inf and you can’t make th
by SassyBird 2y ago
There is no such thing as a uniform distribution over (-inf, +inf) for the simple reason that the Lebesgue measure of (-inf, +inf) is +inf and you can’t make the integral of the whole set be equal to 1. For it to be a valid probabilistic distribution, the integral of 1 over the whole space relative to the distribution should be 1. But it won’t be. In U(a,b) a and b need to be bounded, so that you can divide the Lebesgue measure by (b - a).
- scotty79 2y agoYou can't do it directly, that's what the scaling is for. Another trick would be to answer the question for (a,b) and then see what the answer is when b-a -> inf. For some questions neither of those tricks will work. For this question scaling trick seems to work perfectly.