Markov Inequality And Cut Promotion, Than The Chebyshev Inequality

Almost in all branches of mathematical science, inequalities often paly an important or even pivotal part. In some occasion, its importance is larger than that of equalities. As far as probability theory is concerned, the situation is same, in the paper and literature of this knowledge, some basic inequalities are introduced frequently, so choosing and establishing efficient inequality is often the key to solving problem.Markov's inequality and Chebyshev's inequality are basic inequalities in probability theory, though the proof of them are both easy, they played very important part in the history of probability theory. However, along with rapid develop of probability theory, it's necessary to generalize and improve the former knowledge. Now there are many different kinds of generalization of these two inequalities, this paper discusses them on one hand, extends the Chebyshev's inequality to sums of the form and on the other hand.This paper includes three chapter. The first chapter is a preface, it gives an introduction to Markov's inequality and Chebyshev's inequality, at the same time, it discusses the necessary and sufficient condition of the equalities holding. The second chapter mainly introduces the Markov's inequality of the sums of the form The third chapter extends the Chebyshev's inequality to sums of the form and gives two corresponding corollaries. At last, it gives a Chebyshev's inequality of sums of the form as...