As the title says, I was trying to use the fisher information to find variance for uniform distribution but it seems inconsistent with what one should expect. Can you please give an example. Using Fisher Info for Exp, Poisson, Bernoulli, Normal seem perfectly valid.
The uniform distribution is not a "regular" parametric model since its support depend on the parameter. The likelihood is not differentiable, you can't calculate the Fisher information that is not defined.
I didn't present this case in course, but it is explained in the reference books (see the section i asked you to read).