What is the intuitive meaning behind a random variable being defined as a “lattice”?

In probability theory, a nonnegative random variable X is called a lattice if there exists d0 such that n=0P(X=nd)=1.

Is there a geometric interpretation for why this definition is called a lattice?


It means that X is discrete, and there is some kind of regular spacing to its distribution; that is, the probability mass is concentrated on a finite/countable set of points d,2d,3d,.

Note that not all discrete distributions are lattices. Eg if X can take on the values {1,e,π,5}, this is not a lattice since there is no d such that all the values can be expressed as multiples of d.

Source : Link , Question Author : user1398057 , Answer Author : Hong Ooi

Leave a Comment