# Uniform Distribution

1. Jan 27, 2006

### circa415

If X ~ U(a, b) then f(x) = 1/(b-a)

but what if b-a is less than 1

for instance if X ~ (.5,1) then f(x) = 2???

I'm a bit confused. Any help would be appreciated.

2. Jan 27, 2006

### StatusX

A probability distribution p(x) may take on values greater than one. It doesn't mean something has a probability of more than one of happening because, remember, p(x) isn't itself a probability. The probability that X lies in the range x->x+dx is given by p(x)dx, and as long as the integral of this over any range is not greater than one, which is assured by normalization and the fact that p(x) must be non-negative, the actual probability will never be greater than one.

Last edited: Jan 27, 2006