Abstract: | Let Ω be a finite set with k elements and for each integer let (n-tuple) and and aj ≠ aj+1 for some 1 ≦ j ≦ n ? 1}. Let {Ym} be a sequence of independent and identically distributed random variables such that P(Y1 = a) = k?1 for all a in Ω. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in and in Ω?n with respect to the stochastic process {Ym}. The results here provide us with a better and deeper understanding of the fair coin-tossing (k-sided) process. |