We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.
Let{X(t),t≥0}be a Lévy process with EX(1)=0 and EX^2(1)<∞.In this paper,weshall give two precise asymptotic theorems for{X(t),t≥0}.By the way,we prove the correspondingconclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d.random variables.
