DSpace Kolekcja:
http://hdl.handle.net/11320/3543
2020-05-30T06:48:43Z
2020-05-30T06:48:43Z
Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
Okazaki, Hiroyuki
Shidama, Yasunari
http://hdl.handle.net/11320/3578
2017-10-05T22:54:23Z
2010-01-01T00:00:00Z
Tytuł: Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
Autorzy: Okazaki, Hiroyuki; Shidama, Yasunari
Abstrakt: In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.
2010-01-01T00:00:00Z
Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces
InouĂ©, Takao
Endou, Noboru
Shidama, Yasunari
http://hdl.handle.net/11320/3577
2017-10-05T22:54:26Z
2010-01-01T00:00:00Z
Tytuł: Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces
Autorzy: InouĂ©, Takao; Endou, Noboru; Shidama, Yasunari
Abstrakt: In this article, we define and develop differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [16] and [17]).
2010-01-01T00:00:00Z
Riemann Integral of Functions R into C
Miyajima, Keiichi
Kato, Takahiro
Shidama, Yasunari
http://hdl.handle.net/11320/3576
2017-10-05T22:54:22Z
2010-01-01T00:00:00Z
Tytuł: Riemann Integral of Functions R into C
Autorzy: Miyajima, Keiichi; Kato, Takahiro; Shidama, Yasunari
Abstrakt: In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
2010-01-01T00:00:00Z
Counting Derangements, Non Bijective Functions and the Birthday Problem
Kaliszyk, Cezary
http://hdl.handle.net/11320/3575
2017-10-05T22:57:23Z
2010-01-01T00:00:00Z
Tytuł: Counting Derangements, Non Bijective Functions and the Birthday Problem
Autorzy: Kaliszyk, Cezary
Abstrakt: The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of non-one-to-one functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The article is an extension of [10].
2010-01-01T00:00:00Z