Question

What distribution has values equally distributed between the smallest value and the largest value

Answer 1

The discrete uniform distribution has values equally distributed between the smallest and the largest value. Suppose X be a random variable which takes values 1,2,3,4,...,N. Then X is uniformly distributed between 1 and N so that P( X = i )=1/N for all values of i from 1 to N.

There is also a continuous uniform distribution also called the rectangular distribution. Suppose X be a continuous random variable which follows Uniform(a,b) distribution (a <b).Then the pdf of X is given by f(x)=1/(b-a) for a<x<b