Discrete variable's values are also "disjoint," so we have the gaps in a discrete variable's probability distribution graph. While the formula for the expected value of a discrete variable may seem ...

Let F be a probability distribution on R. Then there exist symmetric (about zero) random variables X and Y whose sum has distribution F if and only if F has mean zero or no mean (finite or infinite).

Jim Pitman, Random Discrete Distributions Invariant under Size-Biased Permutation, Advances in Applied Probability, Vol. 28, No. 2 (Jun., 1996), pp. 525-539 ...

It includes discrete and continuous random variables, their probability distributions and analytical and statistical methods for determining the mean, variance and higher order moments that ...