X and Y are two random variables satisfying P( X = Y) = 1, i.e. X is equal to Y with probability 1. Then their distributions must be identical, i.e., Fx(t) = Fy(t), for all t. Prove Solution I assume U( ) notation means uniform. If X and Y are independent, continuous uniform random variables, then the density of an interval between two points is the same anywhere within the bounds of that distribution. In other words, \"all intervals of the same length on the distribution\'s support are equally probable\" http://en.wikipedia.org/wiki/Uniform_dis.