APPLICATIONS OF SOME COMBINATORIAL PROBLEMS IN PROBABILITY AND STATISTICS

Abstract

The combinatorial application that will be considered in this thesis is a variation of a well known problem known as the matching problem. We will use the number of matches to construct a random variable and study its distribution and

the limiting distribution function . First we give a brief historical remark about the matching problem .

The most famous and early known matching problem is the one due to De Moivre (which appeared in his doctrine of chances ,1714,problem 35) see [18]. There is a considerable literature on the matching problem that has particularly interested psychologists.In [18], the author suggests consulting the papers by D.E.Barton journal of the Royal Statistical Society ,vol . 20 (1958), pp.73- 92 and P.E.Vernon, psychological Bulletin vol.33 (1936),pp .149-77 which give many references. Other references may be found in an editorial note in the American mathematical monthly ,vol.53 (1946). The statement of the problem is as follows:.