摘要
本文证明了如下命题（１）若存在ｋ：２＜ｋ≤ｎ，使Ｘ（ｋ）－Ｘ（１）同｛Ｘ（１）＝１｝及｛Ｘ（１）＝２｝独立，则Ｘ１服从几何分布．（２）若存在ｋ：２＜ｋ≤ｎ，使Ｘ（ｋ）－Ｘ（１）同｛Ｘ（１）＝１｝及｛Ｘ（１）＝３｝独立，则Ｘ１服从几何分布．（３）若存在ｋ：２＜ｋ≤ｎ，使Ｘ（ｋ）－Ｘ（１）同｛Ｘ（１）＝２｝及｛Ｘ（１）＝３｝独立，则Ｘ１服从几何分布．（４）若存在ｋ：２＜ｋ≤ｎ，使Ｘ（ｋ）－Ｘ（１）同｛Ｘ（１）＝１｝及｛Ｘ（１）＝４｝独立，则Ｘ１服从几何分布．
Abstract The following conclusion has been demonstrated in “(1)If there exists a k:2<k≤n, such that X (k) -X (1) is independent of the event {X (1) =1} and {X (1) =2} ,then X 1 is geometric.”;“(2)If there exists a k:2<k≤n ,such that X (k) -X (1) is independent of the event {X (1) =1} and { X (1) =3} ,then X 1 is geometric.”;“(3)If there exists a k:2<k≤n ,such that X (k) -X (1) is independent of the event {X (1) =2 } and {X (1) =3} ,then X 1 is geometric.”;“(4)If there exists a k:2<k≤n ,such that X (k) -X (1) is independent of the event {X (1) =1} and {X (1) =4} ,then X 1 is geometric.”
