Probability And Random Variables

Uysal Bıyıkoğlu, Elif
Axiomatic definition of probability spaces. Combinatorial methods. Conditional probability; product spaces. Random variables; distribution and density functions; multivariate distribution; conditional distributions and densities; independent random variables. Functions of random variables; expected value, moments and characteristic functions.


The Hilbert Space of probability mass functions and applications on probabilistic Inference
Bayramoğlu, Muhammet Fatih; Yılmaz, Ali Özgür; Department of Electrical and Electronics Engineering (2011)
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channe...
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar (AIP Publishing, 2010-06-01)
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
Temporal logic inference for classification and prediction from data
Kong, Zhaodan; Jones, Austin; Medina, Ayala Ana; Aydın Göl, Ebru; Belta, Calin (2014-04-15)
This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of beh...
Time-dependent recursion operators and symmetries
Gurses, M; Karasu, Atalay; Turhan, R (Informa UK Limited, 2002-05-01)
The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed hat he symmetries of he integrable evolution equations obtained through heir recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve his problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion ope...
Set Theory
Kaya, Burak(2018)
Language and axioms of set theory. Ordered pairs, relations and functions. Order relation and well ordered sets. Ordinal numbers, transfinite induction, arithmetic of ordinal numbers. Cardinality and arithmetic of cardinal numbers. Axiom of choice, generalized continuum hypothesis.
Citation Formats
E. Uysal Bıyıkoğlu, “Probability And Random Variables,” 00, 2011, Accessed: 00, 2020. [Online]. Available: