Abstract
The purpose of this paper is to provide some identities derived by moment generating functions and characteristics functions. By using functional equations of the generating functions for the combinatorial numbers y1 (m,n,?), defined in [12, p. 8, Theorem 1], we obtain some new formulas for moments of discrete random variable that follows binomial (Newton) distribution with an application of the Bernstein polynomials. Finally, we present partial derivative formulas for moment generating functions which involve derivative formula of the Bernstein polynomials.
Highlights
Characteristic functions and generating functions such as moment generating functions, ordinary generating functions, and exponential generating functions have been widely used in variety of fields
We briefly introduce some well-known generating functions for the special numbers and polynomials that are used when deriving our identities and formulas
Moment generating function related to binomial (Newton) type distribution including the Bernstein polynomials
Summary
Characteristic functions and generating functions such as moment generating functions, ordinary generating functions, and exponential generating functions have been widely used in variety of fields (namely, probability theory, engineering, and variety branches of mathematics such as discrete mathematics, mathematical statistics, and mathematical physics). The motivation of this paper is to apply characteristic functions and generating functions to the special probability distributions After these applications, we give some formulas and identities. Some restrictions, but aslo the Newton distribution, which is very important probability model when there are two possible outcomes These applications, formulas and identities are associated with well-known special numbers, special polynomials and moments of a random variable of the probability distribution. 2. Moment generating function related to binomial (Newton) type distribution including the Bernstein polynomials. We firstly illustrate that the moment generating function of binomial (Newton) type distribution is related to well-known the Bernstein polynomials. Using this moment generating function, we derive the partial derivative formulas.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
