Asymptotic normality in the problem of selﬁsh parking
In the present work we continue to study one of the models of a discrete analogue of the Renyi problem, known as the “parking problem”. Let n, i be integers satisfying n 0 and 0 i n-1. We place an open interval (i, i+1) in the segment [0, n] with i being a random variable taking values 0, 1, 2, . . . , n-1 with equal probability for all n 2. If n n was studied. In contrast to the classical case, the exact expressions were obtained for the expectation, variance, and third central moments. In this paper the asymptotic behavior of all central moments of the random variable Xn is studied and the asymptotic normality is proved for Xn.