Three isomorphic vector spaces––applicationsto binomial identities, Urn modelsand order statistics Original Research Article

Three isomorphic vector spaces image, image and image are defined. The interplay of these vector spaces leads to easy proofs for binomial identities. Using automorphism each binomial identity is recast into five more identities. Distributions arising out of some stopping rules in drawing balls of two colors from an urn with and without replacement are connected so that one can easily go from one to the other. Identities involving cdfs of order statistics are generalized to those coming from arbitrary multivariate distributions. Discrete distribution similar to binomial is defined, where all the calculations can be done on usual binomial distribution and transferred to the general.