Abstract
The number of successes s_n in n Bernoulli trials increases as n. But the broken line connecting points(n, s_n)shows some peculiar features due to the high correlation between neighboring points. For the special case of cointossing where the probability of success p is equal to 1/2, Feller[1] treats the subject quite impressively. This paper deals with the general case by theoretical computations. The results suggest Propositions on the asymptotic behavior of the distribution of the number of touches(crossings and other contacts)with the theoretical line, and the proportion of the points on one side of the theoretical line.
