Sentence examples for using the probability inequality from inspiring English sources

In this section, we will present some complete convergence for a sequence of acceptable random variables by using the probability inequality.

Using the probability inequalities, we present some moment inequalities, especially the Rosenthal-type inequality for END sequence.

Using the probability inequalities, we can further study the moment inequalities and asymptotic approximation of inverse moment for END sequence.

Using the triangular inequality, we get.

Using the Young inequality, we have (3.7).

Using the Pioncaré inequality, we have (3.22).

Using the (CN) inequality, we have (3.31).

Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality.

Using the Chebyshev-Markov inequality, we can also get the convergence in probability.

Using the inequality (2.11).

Then, using the inequality (218).